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A337044 Numbers k such that both k and sigma(k)=A000203(k) are powerful, i.e., are terms of A001694.

%I A337044 #35 Oct 03 2020 15:27:20
%S A337044 1,81,343,400,9261,27783,32400,137200,189728,224939,972000,1705636,
%T A337044 2205472,3087000,3591200,3648100,3704400,7968032,11113200,13645088,
%U A337044 15350724,15367968,18220059,21161304,24240600,25992000,26680500,29184800,32832900,48586824,51595489
%N A337044 Numbers k such that both k and sigma(k)=A000203(k) are powerful, i.e., are terms of A001694.
%C A337044 From _David A. Corneth_, Aug 14 2020: (Start)
%C A337044 If coprime numbers k and m are in the sequence then k*m is in the sequence.
%C A337044 Up to 10^15, the largest prime divisor of a term is 178987 for which the product of the primes with multiplicity 1 of sigma(178987^2) is 16653 = 3 * 7 * 13 * 61. The second largest prime divisor is 25073 (for which sigma(25073^2) has a product of primes with multiplicity 1 of 341 = 11 * 31), which is quite a bit smaller than 178987. Can we somehow constrain the list of possible prime divisors to ease computation? (End)
%H A337044 David A. Corneth, <a href="/A337044/b337044.txt">Table of n, a(n) for n = 1..10324</a> (terms <= 10^18)
%H A337044 David A. Corneth, <a href="/A337044/a337044.gp.txt">PARI program</a>
%o A337044 (PARI) for(k=1, 60000000, if(ispowerful(k) && ispowerful(sigma(k)), print1(k, ", ")))
%o A337044 (PARI) \\ See Corneth link \\ _David A. Corneth_, Aug 14 2020
%Y A337044 Cf. A000203, A001694, A180090, A337045.
%K A337044 nonn
%O A337044 1,2
%A A337044 _Andrew Howroyd_ and _Hugo Pfoertner_, Aug 12 2020