A325638 Numbers m such that sigma(m) can be obtained as the base-2 carryless product of 2m and some k.

6, 28, 456, 496, 6552, 8128, 30240, 31452, 32760, 429240, 2178540, 7505976, 23569920, 33550336, 45532800, 142990848, 1379454720

Offset: 1

Author

Antti Karttunen, May 21 2019

Keywords

• nonn
• more

Comments

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

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

Conjecture: all terms are even. If this is true, then there are no odd perfect numbers. See also conjectures in A325639 and in A325808.

Links

• Index entries for sequences related to carryless arithmetic.
• Index entries for sequences related to sigma(n).
• Index entries for sequences where any odd perfect numbers must occur.

Crossrefs

Cf. A000203, A091255, A325635, A325637, A325808.

Subsequence of A325639.

Cf. A000396 (a subsequence).

Programs

PARI

A091255sq(a,b) = fromdigits(Vec(lift(gcd(Pol(binary(a))*Mod(1, 2),Pol(binary(b))*Mod(1, 2)))),2);
A325635(n) = A091255sq(n+n, sigma(n));
isA325638(n) = ((n+n)==A325635(n));

Extensions

a(17) from Amiram Eldar, Jun 26 2024