cp's OEIS Frontend

A353365 Numbers k such that the odd part of sigma(sigma(k)) is equal to the odd part of sigma(k).

%I A353365 #19 Apr 18 2022 17:49:03
%S A353365 1,5,12,427,9120,9180,9504,9720,9960,10296,10620,10740,10824,11070,
%T A353365 11310,11480,11484,11556,11628,11748,11934,11960,12024,12036,12072,
%U A353365 12084,12376,12460,12510,12570,12640,12924,12980,13000,13216,13340,13554,13804,13806,13962,13984,14022,14056,14094,14178,14212,14336,14380
%N A353365 Numbers k such that the odd part of sigma(sigma(k)) is equal to the odd part of sigma(k).
%C A353365 Numbers k such that sigma(sigma(k)) = 2^e * sigma(k), for some e >= 0.
%C A353365 Numbers k such that sigma(k) is in A336702.
%C A353365 Numbers k for which A000265(A051027(k)) = A161942(k).
%C A353365 If there existed any hypothetical 3-perfect number (A005820) of the form x = 4u+2 and not divisible by 3, then x would be also included in this sequence, as then sigma(sigma(x)) = 12*x = 4*sigma(x). Such x would be also a term of A349745 and of A351458, and x/2 would be a rare odd term of A000396, and also in A336702. See also the diagram in A347392.
%H A353365 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A353365 (PARI)
%o A353365 A000265(n) = (n>>valuation(n,2));
%o A353365 isA353365(n) = (A000265(sigma(sigma(n)))==A000265(sigma(n)));
%Y A353365 Cf. A000203, A000265, A000396, A005820, A051027, A161942, A336702.
%Y A353365 Subsequence of A066961.
%Y A353365 Cf. also A336700, A336701, A347383, A347392, A349745, A351458 and also A353363.
%K A353365 nonn
%O A353365 1,2
%A A353365 _Antti Karttunen_, Apr 17 2022