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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

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OFFSET

1,1

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

Table of n, a(n) for n=1..42.

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

PROG

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

CROSSREFS

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

Cf. A000396, A002023 (subsequences).

Cf. also A336550 for a similar construction.

Sequence in context: A344754 A364977 A388268 * A336550 A118372 A263928