A378999 Number of trailing 1-bits in the binary representation of sigma(n^2).

1, 3, 1, 5, 5, 2, 1, 7, 1, 1, 1, 2, 3, 4, 2, 9, 2, 4, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 3, 1, 1, 11, 1, 1, 3, 3, 7, 2, 2, 1, 2, 2, 1, 2, 3, 5, 1, 2, 1, 2, 3, 1, 4, 2, 2, 3, 1, 1, 1, 1, 3, 3, 1, 13, 1, 3, 1, 1, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 6, 3, 1, 3, 2, 2, 2, 3, 1, 2, 6, 1, 1, 1, 2

Offset: 1

Author

Antti Karttunen, Dec 16 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to binary expansion of n.
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A000290, A007814, A065764, A378998

Programs

Mathematica

IntegerExponent[DivisorSigma[1, Range[100]^2] + 1, 2] (* Paolo Xausa, Dec 19 2024 *)

PARI

A378999(n) = valuation(sigma(n^2)+1,2);

Formula

a(n) = A378998(A000290(n)).

a(n) = A007814(1+A065764(n)). [the 2-adic valuation of 1+sigma(n^2)]