A378998 Number of trailing 1-bits in the binary representation of sigma(n).

1, 2, 0, 3, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 5, 0, 3, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Antti Karttunen, Dec 16 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences related to binary expansion of n.
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A007814, A088580, A028982 (positions of terms > 0), A028983 (of 0's), A072461 (of 1's), A072462 (of terms > 1), A337195, A378999 [= a(n^2)].

Programs

Mathematica

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

PARI

A378998(n) = valuation(sigma(n)+1,2);

Formula

a(n) = A007814(A088580(n)). [the 2-adic valuation of 1+sigma(n)]

For all n in A028982, a(n) = A337195(n).