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%I #16 Dec 04 2023 01:37:10
%S 0,8,12,45,20,140,28,209,133,308,44,768,52,540,512,897,68,1485,76,
%T 1700,880,1196,92,3536,561,1620,1276,2992,116,5120,124,3713,1904,2660,
%U 1728,8137,148,3276,2560,7844,164,9072,172,6656,5508,4700,188,15120,1485
%N a(n) = A051612(n)*A065387(n) = sigma(n)^2-phi(n)^2, where A051612(n) = sigma(n) - phi(n) and A065387(n) = sigma(n) + phi(n).
%C If n is prime, then a(n) = 4n.
%H Antti Karttunen, <a href="/A077101/b077101.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A077099(n) * A077100(n). - _Antti Karttunen_, May 26 2017
%F From _Amiram Eldar_, Dec 04 2023: (Start)
%F a(n) = A072861(n) - A127473(n).
%F Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = 5*zeta(3)/2 - Product_{p prime}(1 - (2*p-1)/p^3) = (5/2)*A002117 - A065464 = 2.576892... . (End)
%t Table[DivisorSigma[1,n]^2-EulerPhi[n]^2,{n,50}] (* _Harvey P. Dale_, Nov 08 2013 *)
%o (PARI) A077101(n) = (sigma(n)^2 - eulerphi(n)^2); \\ _Antti Karttunen_, May 26 2017
%Y Cf. A000010, A000203, A002117, A051612, A062354, A065387, A065464, A072861, A077099, A077100, A127473.
%K nonn,easy
%O 1,2
%A _Labos Elemer_, Nov 06 2002
%E Edited by _Dean Hickerson_, Nov 07 2002
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