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

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

Author

Antti Karttunen, Apr 17 2022

Keywords

• nonn

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.

Links

• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A000265, A000396, A005820, A051027, A161942, A336702.

Subsequence of A066961.

Cf. also A336700, A336701, A347383, A347392, A349745, A351458 and also A353363.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
isA353365(n) = (A000265(sigma(sigma(n)))==A000265(sigma(n)));