A034778 Dirichlet convolution of Ramanujan numbers (A000594) with themselves.

1, -48, 504, -2368, 9660, -24192, -33488, 239616, -163782, -463680, 1069224, -1193472, -1155476, 1607424, 4868640, 86016, -13811868, 7861536, 21322840, -22874880, -16877952, -51322752, 37286544, 120766464, -27669550, 55462848, -203834232

Offset: 1

Author

N. J. A. Sloane

Keywords

• sign
• mult

Comments

Multiplicative because A000594 is. - Christian G. Bower, May 16 2005

Examples

			G.f. = x - 48*x^2 + 504*x^3 - 2368*x^4 + 9660*x^5 - 24192*x^6 - 33488*x^7 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000594.

Programs

Mathematica

a[n_] := DivisorSum[n, RamanujanTau[#]*RamanujanTau[n/#]&]; Array[a, 30] (* Jean-François Alcover, Nov 14 2015 *)

PARI

{a(n) = local(A); if( n<1, 0, A = Vec( eta(x + x^n*O(x))^24); sumdiv(n, d, A[d] * A[n/d]))}; /* Michael Somos, Jul 16 2004 */

Perl

use ntheory ":all"; for my $n (1..50) { say divisor_sum($n, sub { my $d=shift; ramanujan_tau($d)*ramanujan_tau($n/$d) } # Dana Jacobsen, Sep 05 2015

Formula

a(n) = Sum_{d|n} tau(d)tau(n/d) where tau(n) = A000594(n) is Ramanujan's tau function.