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

Author

Omar E. Pol, Oct 28 2017

Keywords

• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Partial sums give A294016.

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

Cf. A001065, A091818.

Programs

Mathematica

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

PARI

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

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

a(n) = 2*A001065(n) + 1 = A091818(n) + 1. - Omar E. Pol, Dec 01 2024