A361025 a(n) = A007814(sigma(n)) - A007814(n), where A007814(n) gives the 2-adic valuation of n, and sigma is the sum of divisors function.

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

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to sigma(n)

Formula

a(n) = A336937(n) - A007814(n).

Additive with a(2^e) = -e, and for odd primes p, a(p^2e) = 0, a(p^(2e-1)) = A007814(1+p) + A007814(e). - Antti Karttunen, Nov 23 2023

Mathematica

a[n_] := IntegerExponent[DivisorSigma[1, n], 2] - IntegerExponent[n, 2]; Array[a, 100] (* Amiram Eldar, Mar 03 2023 *)

Prog

(PARI) A361025(n) = (valuation(sigma(n), 2) - valuation(n, 2));

Crossrefs

Cf. A000203, A007814, A336937.

Cf. A216780 (positions of 0's), A361024 (their characteristic function), A216781 (positions of terms < 0), A216782 (positions of terms > 0), A324903 (their characteristic function).

Sequence in context: A179541 A057060 A198380 * A152805 A064894 A003638

Adjacent sequences: A361022 A361023 A361024 * A361026 A361027 A361028

Keyword

sign

Author

Antti Karttunen, Mar 03 2023

Status

approved