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

1,1

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.

Cf. A000396, A002023, A326145 (subsequences).

Cf. also A336641 for a similar construction.

Sequence in context: A344754 A364977 A336641 * A118372 A263928 A219362

Adjacent sequences: A336547 A336548 A336549 * A336551 A336552 A336553

Keyword

nonn,more

Author

Antti Karttunen, Jul 28 2020

Status

approved