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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 31 04:27 EST 2023. Contains 359947 sequences. (Running on oeis4.)