A325808 -id:A325808 - cp's OEIS frontend

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

Antti Karttunen, May 21 2019

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.

Cf. A000203, A091255, A325635, A325637, A325808.
Subsequence of A325639.
Cf. A000396 (a subsequence).

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));

a(17) from Amiram Eldar, Jun 26 2024

A325827 a(n) = A325825(2*n, sigma(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 4, 1, 4, 3, 1, 1, 3, 1, 1, 1, 4, 1, 3, 5, 1, 1, 28, 1, 3, 1, 1, 3, 1, 1, 4, 1, 1, 1, 10, 14, 12, 1, 4, 3, 1, 1, 4, 5, 1, 3, 5, 1, 12, 1, 4, 1, 1, 1, 12, 5, 4, 1, 1, 1, 48, 1, 1, 3, 16, 1, 3, 5, 1, 5, 4, 1, 12, 1, 1, 1, 14, 1, 28, 1, 1, 3, 1, 1, 9, 16, 1, 5, 1, 1, 12, 5, 11, 3, 1, 34, 12, 1, 5, 3

Offset: 1

Antti Karttunen, May 22 2019

nonn

See also comment in A325808.

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A000203, A325808, A325825.

Cf. also A325635, A325636.

A004488(n) = subst(Pol(apply(x->(3-x)%3, digits(n, 3)), 'x), 'x, 3);
A325825sq(a,b) = { my(a=fromdigits(Vec(lift(gcd(Pol(digits(a,3))*Mod(1, 3),Pol(digits(b,3))*Mod(1, 3)))),3), b=A004488(a)); min(a,b); };
A325827(n) = A325825sq(n+n, sigma(n));

a(n) = A325825(2*n, A000203(n)).

Terms corrected to agree with the new corrected definition of A325825. - Antti Karttunen, Jan 11 2020

cp's OEIS Frontend

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

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