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.

A356413 Numbers with an equal sum of the even and odd exponents in their prime factorizations.

This page as a plain text file.
%I A356413 #10 Aug 07 2022 07:53:13
%S A356413 1,60,84,90,126,132,140,150,156,198,204,220,228,234,260,276,294,306,
%T A356413 308,315,340,342,348,350,364,372,380,414,444,460,476,490,492,495,516,
%U A356413 522,525,532,550,558,564,572,580,585,620,636,644,650,666,693,708,726,732,735
%N A356413 Numbers with an equal sum of the even and odd exponents in their prime factorizations.
%C A356413 Numbers k such that A350386(k) = A350387(k).
%C A356413 A085987 is a subsequence. Terms that are not in A085987 are 1, 2160, 3024, ...
%H A356413 Amiram Eldar, <a href="/A356413/b356413.txt">Table of n, a(n) for n = 1..10000</a>
%e A356413 60 is a term since A350386(60) = A350387(60) = 2.
%t A356413 f[p_, e_] := (-1)^e*e; q[1] = True; q[n_] := Plus @@ f @@@ FactorInteger[n] == 0; Select[Range[1000], q]
%o A356413 (PARI) isok(n) = {my(f = factor(n)); sum(i = 1, #f~, (-1)^f[i,2]*f[i,2]) == 0};
%Y A356413 Cf. A350386, A350387.
%Y A356413 Subsequence of A028260.
%Y A356413 Subsequences: A085987, A179698, A190109, A190110.
%Y A356413 Similar sequences: A048109, A187039, A348097.
%K A356413 nonn
%O A356413 1,2
%A A356413 _Amiram Eldar_, Aug 06 2022