A224225 a(0)=1; thereafter a(n) = 2*s(n,1)-3*s(n,2)+4*s(n,4)+9*s(n,6)-36*s(n,12), where s(n,k) = sigma(n/k) if k divides n, otherwise 0.

1, 2, 3, 8, 9, 12, 21, 16, 21, 26, 18, 24, 27, 28, 24, 48, 45, 36, 75, 40, 54, 64, 36, 48, 39, 62, 42, 80, 72, 60, 126, 64, 93, 96, 54, 96, 81, 76, 60, 112, 126, 84, 168, 88, 108, 156, 72, 96, 63, 114, 93, 144, 126, 108, 237, 144, 168, 160, 90, 120, 162, 124, 96, 208, 189, 168, 252, 136, 162, 192, 144, 144, 93, 148, 114, 248, 180, 192, 294, 160, 270

Offset

0,2

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

K. S. Williams, The parents of Jacobi's four squares theorem are unique, Amer. Math. Monthly, 120 (2013), 329-345.

Mathematica

s[n_, k_] := If[Divisible[n, k], DivisorSigma[1, n/k], 0]; a[0] = 1; a[n_] := 2*s[n, 1] - 3*s[n, 2] + 4*s[n, 4] + 9*s[n, 6] - 36*s[ n, 12]; Array[a, 100, 0] (* Amiram Eldar, Aug 17 2019 *)

Prog

(PARI) s(n, k) = if (!(n%k), sigma(n/k), 0);
a(n) = if (n==0, 1, 2*s(n, 1)-3*s(n, 2)+4*s(n, 4)+9*s(n, 6)-36*s(n, 12)); \\ Michel Marcus, Sep 27 2017

Crossrefs

Cf. A000203.

Sequence in context: A284370 A273783 A075190 * A283160 A281148 A284791

Adjacent sequences: A224222 A224223 A224224 * A224226 A224227 A224228

Keyword

nonn

Author

N. J. A. Sloane, Apr 09 2013

Status

approved