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

1,2

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.

Links

Table of n, a(n) for n=1..48.

Index entries for sequences related to sigma(n)

Prog

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

Sequence in context: A330218 A047658 A290804 * A146542 A264873 A116058

Adjacent sequences: A353362 A353363 A353364 * A353366 A353367 A353368

Keyword

nonn

Author

Antti Karttunen, Apr 17 2022

Status

approved