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A180090 Sigma-powerful numbers: powerful numbers n such that sigma(n) is also powerful. An incomplete version of A337045. 6
81, 343, 400, 1705636, 3648100, 13645088, 25992000, 26680500, 29184800, 80802000, 110215125, 178054848, 180093375, 213444000, 310144500, 408632609, 575664500, 1055340196, 1120504500, 1476326929, 1667329664, 2066544500 (list; graph; refs; listen; history; text; internal format)
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

nonn,dead

AUTHOR

Walter Kehowski, Aug 09 2010

STATUS

approved

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Last modified June 22 12:27 EDT 2021. Contains 345379 sequences. (Running on oeis4.)