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%I #28 Jul 11 2019 00:15:37
%S 6,28,456,496,6552,8128,30240,31452,32760,429240,2178540,7505976,
%T 23569920,33550336,45532800,142990848
%N Numbers n such that sigma(n) can be obtained as the base-2 carryless product of 2n and some k.
%C Numbers n such that A000203(n) = A048720(2n, k) for some k.
%C Numbers n for which A091255(2n, sigma(n)) = 2n.
%C Conjecture: all terms are even. If this is true, then there are no odd perfect numbers. See also conjectures in A325639 and in A325808.
%H <a href="/index/Ca#CARRYLESS">Index entries for sequences related to carryless arithmetic</a>
%H <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o (PARI)
%o A091255sq(a,b) = fromdigits(Vec(lift(gcd(Pol(binary(a))*Mod(1, 2),Pol(binary(b))*Mod(1, 2)))),2);
%o A325635(n) = A091255sq(n+n, sigma(n));
%o isA325638(n) = ((n+n)==A325635(n));
%Y Cf. A000203, A091255, A325635, A325637, A325808.
%Y Subsequence of A325639.
%Y Cf. A000396 (a subsequence).
%K nonn,more
%O 1,1
%A _Antti Karttunen_, May 21 2019
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