A294015 Sum of the even divisors of 2n, minus the (n-1)st odd number.

1, 3, 3, 7, 3, 13, 3, 15, 9, 17, 3, 33, 3, 21, 19, 31, 3, 43, 3, 45, 23, 29, 3, 73, 13, 33, 27, 57, 3, 85, 3, 63, 31, 41, 27, 111, 3, 45, 35, 101, 3, 109, 3, 81, 67, 53, 3, 153, 17, 87, 43, 93, 3, 133, 35, 129, 47, 65, 3, 217, 3, 69, 83, 127, 39, 157, 3, 117, 55, 149, 3, 247, 3, 81, 99, 129, 39, 181, 3, 213, 81, 89, 3, 281

Offset

1,2

Comments

a(n) = 3 if and only if n is prime.

Links

Table of n, a(n) for n=1..84.

Formula

a(n) = A074400(n) - A005408(n-1) = 2*A000203(n) - 2*n + 1 = A000203(n) - A235796(n).

Sum_{k=1..n} a(k) = (Pi^2/6 - 1) * n^2 + O(n*log(n)). - Amiram Eldar, Mar 30 2024

Mathematica

a[n_] := 2*(DivisorSigma[1, n] - n) + 1; Array[a, 100] (* Amiram Eldar, Mar 30 2024 *)

Prog

(PARI) a(n) = 2*sigma(n) - 2*n + 1; \\ Michel Marcus, Oct 29 2017

Crossrefs

Partial sums give A294016.

Cf. A000203, A013661, A005408, A074400, A235796, A294017.

Sequence in context: A323774 A062402 A347405 * A156838 A274845 A324048

Adjacent sequences: A294012 A294013 A294014 * A294016 A294017 A294018

Keyword

nonn

Author

Omar E. Pol, Oct 28 2017

Status

approved