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

Author

Leroy Quet, Dec 08 2009

Keywords

• nonn

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

Crossrefs

Cf. A001597, A175051.

Programs

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