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%I #11 Apr 23 2024 08:29:02
%S -1,-2,-1,-3,0,-4,3,-2,3,1,10,-3,14,7,11,7,24,7,30,12,26,26,43,11,44,
%T 38,45,34,64,27,72,47,67,66,77,40,98,82,92,63,117,69,127,93,105,117,
%U 147,78,151,121,149,129,180,121,175,134,181,178,215,114,227,200
%N a(n) = floor(6*n*sqrt(n)/Pi^2) - sigma(n), where sigma(n) is the sum of the divisors of n (A000203).
%C Always > 0 for n > 12.
%D József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter III, p. 77, section III.1.1.c.
%t a[n_] := Floor[n * Sqrt[n] / Zeta[2]] - DivisorSigma[1, n]; Array[a, 100] (* _Amiram Eldar_, Apr 23 2024 *)
%o (PARI) a(n)=6*n*sqrt(n)\Pi^2 - sigma(n) \\ _Charles R Greathouse IV_, Feb 14 2013
%Y Cf. A000203, A057641, A055682, A059956.
%K sign
%O 1,2
%A _N. J. A. Sloane_, Nov 29 2000
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