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A224226 a(0)=1; thereafter a(n) =s(n,3)-s(n,4)-s(n,6)+s(n,12), where s(n,k) = sigma(n/k) if k divides n, otherwise 0. 2
1, 0, 0, 1, -1, 0, 2, 0, -3, 4, 0, 0, 1, 0, 0, 6, -7, 0, 8, 0, -6, 8, 0, 0, -1, 0, 0, 13, -8, 0, 12, 0, -15, 12, 0, 0, 7, 0, 0, 14, -18, 0, 16, 0, -12, 24, 0, 0, -5, 0, 0, 18, -14, 0, 26, 0, -24, 20, 0, 0, 6, 0, 0, 32, -31, 0, 24, 0, -18, 24, 0, 0, 5, 0, 0, 31, -20, 0, 28 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

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.

MAPLE

s := proc(n, k)

if modp(n, k) = 0 then

numtheory[sigma](n/k) ;

else

0 ;

end if;

end proc:

A224226 := proc(n)

if n = 0 then

1;

else

s(n, 3)-s(n, 4)-s(n, 6)+s(n, 12) ;

end if;

end proc: # R. J. Mathar, Nov 14 2018

MATHEMATICA

s[n_, k_] := If[Divisible[n, k], DivisorSigma[1, n/k], 0]; a[0] = 1; a[n_] := s[n, 3] - s[n, 4] - s[n, 6] + 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, s(n, 3)-s(n, 4)-s(n, 6)+s(n, 12)); \\ Michel Marcus, Sep 27 2017

CROSSREFS

Cf. A000203, A321527.

Sequence in context: A021835 A112476 A321527 * A153250 A102389 A099091

Adjacent sequences: A224223 A224224 A224225 * A224227 A224228 A224229

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Apr 09 2013

STATUS

approved

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Last modified February 7 22:58 EST 2023. Contains 360132 sequences. (Running on oeis4.)