A175050 Positive integers n where both n and the number of divisors of n are perfect powers. (Both n and d(n) are elements of A001597.)
1, 8, 27, 36, 100, 125, 128, 196, 216, 225, 256, 343, 441, 484, 676, 900, 1000, 1089, 1156, 1225, 1296, 1331, 1444, 1521, 1764, 2116, 2187, 2197, 2304, 2601, 2744, 3025, 3249, 3364, 3375, 3844, 4225, 4356, 4761, 4900, 4913, 5476, 5929, 6084, 6400, 6561
Offset: 1
Keywords
Examples
128 has 8 divisors. Since 128 is a perfect power (128 = 2^7), and since 8 is also a perfect power (8 = 2^3), then 128 is in this sequence.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Block[{nn = 10^4, s}, s = Union@ Flatten@ Table[n^e, {e, Prime@ Range@ PrimePi@ Log2@ nn}, {n, nn^(1/e)}]; Select[s, MemberQ[s, DivisorSigma[0, #]] &]] (* Michael De Vlieger, Nov 24 2017, after T. D. Noe at A001597 *)
Extensions
Extended by Ray Chandler, Dec 10 2009
Comments