cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A345004 #11 Jun 07 2021 06:50:21
%S A345004 6,28,496,5292,8128,33550336
%N A345004 Numbers k such that A345001(k)*A048250(k) is equal to A342001(k)*A344753(k) and A345001(n)/A342001(n) is an integer.
%C A345004 Equally, we may require that A344753(k)/A048250(k) is an integer, thus this is a subsequence of A344754.
%H A345004 <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%o A345004 (PARI)
%o A345004 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A345004 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A345004 A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
%o A345004 A344753(n) = sumdiv(n,d,(d<n)*(d+(issquarefree(n/d) * d)));
%o A345004 A342001(n) = (A003415(n) / A003557(n));
%o A345004 A345001(n) = (sigma(n)+A003415(n)-(2*n));
%o A345004 isA345004(n) = { my(u=A345001(n),v=A342001(n)); (v>0&&1==denominator(u/v)&&(u*A048250(n) == v*A344753(n))); };
%Y A345004 Cf. A000396 (subsequence), A003415, A003557, A048250, A342001, A344753, A345001.
%Y A345004 Intersection of A344754 and A345003.
%K A345004 nonn,more
%O A345004 1,1
%A A345004 _Antti Karttunen_, Jun 05 2021