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.

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

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: A112476 A370724 A321527 * A153250 A102389 A099091

Adjacent sequences: A224223 A224224 A224225 * A224227 A224228 A224229

Keyword

sign

Author

N. J. A. Sloane, Apr 09 2013

Status

approved