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%I #10 Sep 08 2022 08:45:08
%S -1,0,12,38,54,180,120,457,514,1006,324,1764,462,2816,2952,4044,810,
%T 6381,1020,8470,7840,10924,1512,15356,7724,17990,14544,23168,2430,
%U 30728,2784,33137,29232,40066,29456,52804,3990,55844,47656,69102,4914,84448,5412,89020
%N a(n) = sigma[k](n) - phi(n)^k - d(n)^k for k=3.
%C It is known that a(n) >= 0 for n >= 2.
%D D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, p. 10.
%H T. D. Noe, <a href="/A079539/b079539.txt">Table of n, a(n) for n=1..10000</a>
%F a(n) = 3*n^2 - 3*n - 6 for prime n. - _T. D. Noe_, Dec 19 2006
%t Table[DivisorSigma[3,n] - EulerPhi[n]^3 - DivisorSigma[0, n]^3, {n, 80}] (* _G. C. Greubel_, Jan 15 2019 *)
%o (PARI) vector(80, n, sigma(n,3) - eulerphi(n)^3 - numdiv(n)^3) \\ _G. C. Greubel_, Jan 15 2019
%o (Magma) [DivisorSigma(3,n) - EulerPhi(n)^3 - DivisorSigma(0,n)^3: n in [1..80]]; // _G. C. Greubel_, Jan 15 2019
%o (Sage) [sigma(n,3) - euler_phi(n)^3 - sigma(n,0)^3 for n in (1..80)] # _G. C. Greubel_, Jan 15 2019
%Y Cf. A000010, A000005, A000203, A046520 (for k=1), A079538.
%K sign
%O 1,3
%A _N. J. A. Sloane_, Jan 23 2003
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