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

1,1

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: A293453 A344754 A364977 * A336550 A118372 A263928

Adjacent sequences: A336638 A336639 A336640 * A336642 A336643 A336644

Keyword

nonn

Author

Antti Karttunen, Jul 28 2020

Status

approved