A336550 - OEIS

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

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OFFSET

1,1

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

Table of n, a(n) for n=1..27.

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

PROG

(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)); };

CROSSREFS

Intersection of A175200 and A336552.

Cf. A007947, A326143, A336551.