A336550 Numbers k such that A007947(k) divides sigma(k) and A003557(k)-1 either divides A326143(k) [= A001065(k) - A007947(k)], or both are zero.

6, 24, 28, 96, 120, 234, 384, 496, 936, 1536, 1638, 6144, 8128, 24576, 42588, 98304, 393216, 1089270, 1572864, 6291456, 25165824, 33550336, 100663296, 115048440, 402653184, 1185125760, 1610612736

Offset: 1

Author

Antti Karttunen, Jul 28 2020

Keywords

• nonn
• more

Comments

Numbers k such that gcd(sigma(k)-A007947(k), A007947(k)) == A007947(k) are those in A175200. These are equal to k such that gcd(A326143(k), A007947(k)) = gcd(sigma(k)-A007947(k)-k, A007947(k)) are equal to A007947(k).

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

Intersection of A175200 and A336552.

Cf. A007947, A326143, A336551.

Cf. A000396, A002023, A326145 (subsequences).

Cf. also A336641 for a similar construction.

Programs

PARI

A007947(n) = factorback(factorint(n)[, 1]);
isA336550(n) = { my(r=A007947(n), s=sigma(n), u=((n/r)-1)); (!(s%r) && (gcd(u,(s-r-n))==u)); };