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%I #22 Jul 29 2020 16:38:03
%S 6,24,28,96,120,234,384,496,936,1536,1638,6144,8128,24576,42588,98304,
%T 393216,1089270,1572864,6291456,25165824,33550336,100663296,115048440,
%U 402653184,1185125760,1610612736
%N Numbers k such that A007947(k) divides sigma(k) and A003557(k)-1 either divides A326143(k) [= A001065(k) - A007947(k)], or both are zero.
%C Numbers k such that gcd(sigma(k)-A007947(k), A007947(k)) == A007947(k) are those in A175200. These are equal to k such that gcd(A326143(k), A007947(k)) = gcd(sigma(k)-A007947(k)-k, A007947(k)) are equal to A007947(k).
%C Sequence is infinite because all numbers of the form 6*4^n (A002023) are present.
%C Question: Are there any odd terms?
%H <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%o (PARI)
%o A007947(n) = factorback(factorint(n)[, 1]);
%o isA336550(n) = { my(r=A007947(n), s=sigma(n), u=((n/r)-1)); (!(s%r) && (gcd(u,(s-r-n))==u)); };
%Y Intersection of A175200 and A336552.
%Y Cf. A007947, A326143, A336551.
%Y Cf. A000396, A002023, A326145 (subsequences).
%Y Cf. also A336641 for a similar construction.
%K nonn,more
%O 1,1
%A _Antti Karttunen_, Jul 28 2020
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