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A353365
Numbers k such that the odd part of sigma(sigma(k)) is equal to the odd part of sigma(k).
5
1, 5, 12, 427, 9120, 9180, 9504, 9720, 9960, 10296, 10620, 10740, 10824, 11070, 11310, 11480, 11484, 11556, 11628, 11748, 11934, 11960, 12024, 12036, 12072, 12084, 12376, 12460, 12510, 12570, 12640, 12924, 12980, 13000, 13216, 13340, 13554, 13804, 13806, 13962, 13984, 14022, 14056, 14094, 14178, 14212, 14336, 14380
OFFSET
1,2
COMMENTS
Numbers k such that sigma(sigma(k)) = 2^e * sigma(k), for some e >= 0.
Numbers k such that sigma(k) is in A336702.
Numbers k for which A000265(A051027(k)) = A161942(k).
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.
PROG
(PARI)
A000265(n) = (n>>valuation(n, 2));
isA353365(n) = (A000265(sigma(sigma(n)))==A000265(sigma(n)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 17 2022
STATUS
approved