OFFSET
1,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..1000
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
EXAMPLE
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 +...
MAPLE
with(numtheory); A195735:=n->2*sigma(n^2) - sigma(n)^2; seq(A195735(n), n=1..100); # Wesley Ivan Hurt, Mar 04 2014
MATHEMATICA
Table[2 DivisorSigma[1, n^2] - DivisorSigma[1, n]^2, {n, 100}] (* Wesley Ivan Hurt, Mar 04 2014 *)
PROG
(PARI) {a(n)=2*sigma(n^2) - sigma(n)^2}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Sep 22 2011
STATUS
approved