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

Author

Walter Kehowski, Aug 09 2010

Keywords

• dead

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.

Examples

			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.
		

Links

• Walter A. Kehowski, Table of n, a(n) for n = 1..1536
• Walter A. Kehowski, Sigma-powerful numbers

Crossrefs

Cf. A001694, A000203, A128607.