%I #33 Jun 26 2024 06:01:29

%S 6,28,456,496,6552,8128,30240,31452,32760,429240,2178540,7505976,

%T 23569920,33550336,45532800,142990848,1379454720

%N Numbers m such that sigma(m) can be obtained as the base-2 carryless product of 2m and some k.

%C Numbers m such that A000203(m) = A048720(2m, k) for some k.

%C Numbers m for which A091255(2m, sigma(m)) = 2m.

%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/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

%H <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</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

%E a(17) from _Amiram Eldar_, Jun 26 2024