Python Challenges: Get number of distinct terms generated by a^b

Last update on December 21 2024 07:49:51 (UTC/GMT +8 hours)

Consider all integer combinations of a^b for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
2²=4, 2³=8, 2⁴=16, 2⁵=32
3²=9, 3³=27, 3⁴=81, 3⁵=243
4²=16, 4³=64, 4⁴=256, 4⁵=1024
5²=25, 5³=125, 5⁴=625, 5⁵=3125
If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
Write a Python program to get number of distinct terms generated by a^b for 2 ≤ a ≤ 21 and 2 ≤ b ≤ 21. Also print all the distinct numbers.

Sample Solution:

Python Code:

def compute_distinct_num():
	nums = set(a**b for a in range(2, 21) for b in range(2, 21))
	return str(len(nums)), nums
x,y = compute_distinct_num()
print("Number of distinct elements:", x)
print("\nDistinct elements are:")
print(y)

Sample Output:

Number of distinct elements: 324

Distinct elements are:
{512, 1024, 2048, 4096, 4, 8192, 32768, 65536, 8, 131072, 262144, 524288, 9, 1048576, 274877906944, 1099511627776, 16, 26623333280885243904, 38416, 30491346729331195904, 332525673007965087890625, 10000000000000000000, 16384, 104976, 104127350297911241532841, 25, 31381059609, 27, 5480386857784802185939, 262144000000000000000000, 16777216, 32, 67108864, 268435456, 1073741824, 4294967296, 17179869184, 68719476736, 36, 13841287201, 12157665459056928801, 1771561, 100000000000000000000, 18446744073709551616, 75557863725914323419136, 1208925819614629174706176, 95367431640625, 10077696, 49, 121439531096594251776, 3125, 2213314919066161, 4747561509943, 3570467226624, 13107200000000000000000, 34522712143931, 793714773254144, 3656158440062976, 64, 46656, 1000000, 665416609183179841, 7529536, 4722366482869645213696, 2821109907456, 10000000000000000, 429981696, 2177953337809371136, 83521, 505447028499293771, 2476099, 25600000000, 20822964865671168, 1461920290375446110677, 759375, 81, 244140625, 678223072849, 1000000000, 1419857, 4064231406647572522401601, 12748236216396078174437376, 371293, 2097152, 7776, 248832, 576650390625, 1477891880035400390625, 100, 612220032, 14348907, 15407021574586368, 625, 20661046784, 827240261886336764177, 121, 893871739, 125, 3833759992447475122176, 128, 2176782336, 1853020188851841, 10000000, 1000000000000, 2985984, 100000000000000000, 232630513987207, 56693912375296, 16677181699666569, 379749833583241, 2187, 319479999370622926848, 295147905179352825856, 160000, 38443359375, 144, 3138428376721, 118587876497, 198359290368, 204800000000000, 2197, 100000000000000, 1977326743, 8589934592, 549755813888, 4398046511104, 4194304, 35184372088832, 281474976710656, 2251799813685248, 18014398509481984, 144115188075855872, 1152921504606846976, 100000, 11390625, 39346408075296537575424, 59049, 169, 64000000, 35831808, 2744, 205891132094649, 4826809, 426878854210636742656, 512000000000, 288441413567621167681, 1728, 362797056, 5764801, 45949729863572161, 196, 762939453125, 582622237229761, 5832, 6859, 1946195068359375, 19004963774880799438801, 150094635296999121, 9904578032905937, 1280000000, 216, 729, 25937424601, 48828125, 537824, 79792266297612001, 282429536481, 19683, 225, 15181127029874798299, 155568095557812224, 96889010407, 5976303958948914397184, 282475249, 243, 823543, 9765625, 47045881, 256, 1679616, 13060694016, 100000000, 10000000000000, 20736, 101559956668416, 1000000000000000000, 5159780352, 15625, 1475789056, 6568408355712890625, 11019960576, 2218611106740436992, 17592186044416, 4503599627370496, 1296, 10000, 72057594037927936, 130321, 672749994932560009201, 11112006825558016, 48661191875666868481, 374813367582081024, 112455406951957393129, 799006685782884121, 161051, 134217728, 1978419655660313589123979, 655360000000000000000, 1889568, 60466176, 10000000000, 289, 34012224, 16983563041, 815730721, 2357947691, 116490258898219, 78125, 3375, 22876792454961, 14641, 1331, 4913, 1792160394037, 239072435685151324847153, 37589973457545958193355601, 98526125335693359375, 5559917313492231481, 19073486328125, 61917364224, 8000, 43046721, 100000000000, 129746337890625, 324, 10240000000000, 40353607, 387420489, 1156831381426176, 8650415919381337933, 285311670611, 343, 6746640616477458432, 1350851717672992089, 3200000, 106993205379072, 2401, 214358881, 24137569, 32768000000000000000, 1953125, 470184984576, 62748517, 361, 6975757441, 170859375, 410338673, 322687697779, 29192926025390625, 64268410079232, 4782969, 279936, 33232930569601, 105413504, 2562890625, 16926659444736, 6131066257801, 30517578125, 61159090448414546291, 184884258895036416, 400, 3486784401, 117649, 28561, 1220703125, 78364164096, 289254654976, 1283918464548864, 1638400000000000000, 743008370688, 6561, 2015993900449, 42052983462257059, 1000000000000000, 16807, 8916100448256, 10604499373, 4096000000000000, 8649755859375, 104857600000000000000000000, 1628413597910449, 23298085122481, 34271896307633, 2185911559738696531968, 51185893014090757, 83668255425284801560576, 22168378200531005859375, 152587890625, 4049565169664, 129140163, 19487171, 50625, 5242880000000000000000000, 137858491849, 708235345355337676357632, 609359740010496, 1594323, 11398895185373143, 3814697265625, 3937376385699289, 1162261467, 81920000000000000, 390625, 168377826559400929, 4177248169415651, 1000, 6103515625, 2541865828329, 437893890380859375, 531441, 2862423051509815793, 14063084452067724991009, 177147, 302875106592253}

Flowchart:

#Ref. https://bit.ly/2vaWX1y

Python Code Editor:

Contribute your code and comments through Disqus.

Previous: Write a Python program to compute the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed.
Next: Write a Python program to find the sum of all the numbers that can be written as the sum of fifth powers of their digits.