A195735 a(n) = 2*sigma(n^2) - sigma(n)^2.
1, 5, 10, 13, 26, 38, 50, 29, 73, 110, 122, 22, 170, 222, 230, 61, 290, 173, 362, 158, 458, 566, 530, -298, 601, 798, 586, 398, 842, 458, 962, 125, 1154, 1382, 1230, -779, 1370, 1734, 1622, -226, 1682, 1158, 1850, 1190, 1418, 2558, 2210, -2090, 2353, 2285, 2798, 1742, 2810, 902, 3062, 78, 3506, 4094, 3482, -3238
Offset: 1
Keywords
Examples
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 +... 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 +...
Links
- Paul D. Hanna, Table of n, a(n) for n = 1..1000
Programs
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Maple
with(numtheory); A195735:=n->2*sigma(n^2) - sigma(n)^2; seq(A195735(n), n=1..100); # Wesley Ivan Hurt, Mar 04 2014
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Mathematica
Table[2 DivisorSigma[1, n^2] - DivisorSigma[1, n]^2, {n, 100}] (* Wesley Ivan Hurt, Mar 04 2014 *) -
PARI
{a(n)=2*sigma(n^2) - sigma(n)^2}
Formula
a(n) < 0 for n found in A067807.
Equals the logarithmic derivative of A195734.
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