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%I #27 Feb 18 2023 10:25:05
%S 81,343,400,1705636,3648100,13645088,25992000,26680500,29184800,
%T 80802000,110215125,178054848,180093375,213444000,310144500,408632609,
%U 575664500,1055340196,1120504500,1476326929,1667329664,2066544500
%N Sigma-powerful numbers: powerful numbers n such that sigma(n) is also powerful. An incomplete version of A337045.
%C 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.
%H Walter A. Kehowski, <a href="/A180090/b180090.txt">Table of n, a(n) for n = 1..1536</a>
%H Walter A. Kehowski, <a href="http://web.gccaz.edu/~walof42631/Sigma-powerful-numbers.html">Sigma-powerful numbers</a>
%e 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.
%Y Cf. A001694, A000203, A128607.
%K dead
%O 1,1
%A _Walter Kehowski_, Aug 09 2010
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