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%I #15 Mar 17 2024 03:17:32
%S 1,5,10,13,26,38,50,29,73,110,122,22,170,222,230,61,290,173,362,158,
%T 458,566,530,-298,601,798,586,398,842,458,962,125,1154,1382,1230,-779,
%U 1370,1734,1622,-226,1682,1158,1850,1190,1418,2558,2210,-2090,2353,2285,2798,1742,2810,902,3062,78,3506,4094,3482,-3238
%N a(n) = 2*sigma(n^2) - sigma(n)^2.
%H Paul D. Hanna, <a href="/A195735/b195735.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) < 0 for n found in A067807.
%F Equals the logarithmic derivative of A195734.
%F Sum_{k=1..n} a(k) ~ c * n^3, where c = (10/Pi^2-5/6)*zeta(3) = 0.216224196369... . - _Amiram Eldar_, Mar 17 2024
%e L.g.f.: L(x) = x + 5*x^2/2 + 10*x^3/3 + 13*x^4/4 + 26*x^5/5 + 38*x^6/6 +...
%e where exp(L(x)) = 1 + x + 3*x^2 + 6*x^3 + 11*x^4 + 22*x^5 + 40*x^6 + 72*x^7 + 123*x^8 + 215*x^9 + 363*x^10 +...+ A195734(n)*x^n +...
%p with(numtheory); A195735:=n->2*sigma(n^2) - sigma(n)^2; seq(A195735(n), n=1..100); # _Wesley Ivan Hurt_, Mar 04 2014
%t Table[2 DivisorSigma[1, n^2] - DivisorSigma[1, n]^2, {n, 100}] (* _Wesley Ivan Hurt_, Mar 04 2014 *)
%o (PARI) {a(n)=2*sigma(n^2) - sigma(n)^2}
%Y Cf. A195734 (exp), A067807, A065764, A000203, A002117.
%K sign
%O 1,2
%A _Paul D. Hanna_, Sep 22 2011
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