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

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

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.

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 *)

Crossrefs

Cf. A001597, A175051.

Sequence in context: A371955 A066215 A086213 * A131548 A063142 A235994

Adjacent sequences: A175047 A175048 A175049 * A175051 A175052 A175053

Keyword

nonn

Author

Leroy Quet, Dec 08 2009

Extensions

Extended by Ray Chandler, Dec 10 2009

Status

approved