A336641 Numbers k such that A007913(k) divides sigma(k) and A008833(k)-1 either divides A326127(k) (= sigma(k)-core(k)-k), or both are zero.

6, 24, 28, 96, 120, 150, 294, 384, 496, 1014, 1536, 3276, 3750, 3780, 6144, 8128, 14406, 20328, 24576, 32760, 93750, 98304, 171366, 306180, 393216, 705894, 1241460, 1572864, 2343750, 6291456, 16380000, 24800580, 25165824, 28960854, 30387840, 33550336, 34588806, 58593750, 100663296, 165143160, 332226048, 402653184

Offset: 1

Author

Antti Karttunen, Jul 28 2020

Keywords

• nonn

Comments

Numbers k such that A326128(k) = A326129(k) form a subsequence of this sequence. So far it is not known whether it contains any other terms apart from those of A000396. See comments in A326129.

Sequence is infinite because all numbers of the form 6*4^n (A002023) are present.

Question: Are there any odd terms?

Links

• Index entries for sequences where odd perfect numbers must occur, if they exist at all

Crossrefs

Cf. A000203, A007913, A228058, A326126, A326127, A326128, A326129, A336642.

Cf. A000396, A002023 (subsequences).

Cf. also A336550 for a similar construction.

Programs

PARI

isA336641(n) = { my(c=core(n), s=sigma(n), u=((n/c)-1)); (!(s%c) && (gcd(u,(s-c-n))==u)); };