A345004 Numbers k such that A345001(k)*A048250(k) is equal to A342001(k)*A344753(k) and A345001(n)/A342001(n) is an integer.

6, 28, 496, 5292, 8128, 33550336

Offset

1,1

Comments

Equally, we may require that A344753(k)/A048250(k) is an integer, thus this is a subsequence of A344754.

Links

Table of n, a(n) for n=1..6.

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

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));
A344753(n) = sumdiv(n, d, (d<n)*(d+(issquarefree(n/d) * d)));
A342001(n) = (A003415(n) / A003557(n));
A345001(n) = (sigma(n)+A003415(n)-(2*n));
isA345004(n) = { my(u=A345001(n), v=A342001(n)); (v>0&&1==denominator(u/v)&&(u*A048250(n) == v*A344753(n))); };

Crossrefs

Cf. A000396 (subsequence), A003415, A003557, A048250, A342001, A344753, A345001.

Intersection of A344754 and A345003.

Sequence in context: A138876 A326145 A174633 * A370789 A351440 A325637

Adjacent sequences: A345001 A345002 A345003 * A345005 A345006 A345007

Keyword

nonn,more

Author

Antti Karttunen, Jun 05 2021

Status

approved