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

Author

Antti Karttunen, Jun 05 2021

Keywords

• nonn
• more

Comments

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

Links

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

Crossrefs

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

Intersection of A344754 and A345003.

Programs

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,(dA342001(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))); };