A180090 Sigma-powerful numbers: powerful numbers n such that sigma(n) is also powerful. An incomplete version of A337045.

81, 343, 400, 1705636, 3648100, 13645088, 25992000, 26680500, 29184800, 80802000, 110215125, 178054848, 180093375, 213444000, 310144500, 408632609, 575664500, 1055340196, 1120504500, 1476326929, 1667329664, 2066544500

Offset

1,1

Comments

The list is not exhaustive since the search was restricted to sigma(p^k) such that p<1728 and all powers k such that all primes in the factorization of sigma(p^k) are also less than 1728.

Links

Walter A. Kehowski, Table of n, a(n) for n = 1..1536

Walter A. Kehowski, Sigma-powerful numbers

Example

sigma(3^4)=11^2, sigma(7^3)=2^4*5^2, sigma(2^4*5^2)=31^2, sigma(2^2*653^2)=7^2*13^2*19^2.

Crossrefs

Cf. A001694, A000203, A128607.

Sequence in context: A337044 A337045 A128607 * A217967 A237384 A237249

Adjacent sequences: A180087 A180088 A180089 * A180091 A180092 A180093

Keyword

dead

Author

Walter Kehowski, Aug 09 2010

Status

approved