OFFSET
1,1
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..1000
FORMULA
Equals the logarithmic derivative of A195584.
a(n) = A054785(n^2), where A054785 is the logarithmic derivative of A015128, which is the number of overpartitions of n.
Sum_{k=1..n} a(k) ~ c * n^3, where c = 7*zeta(3)/Pi^2 = 0.85255679763501158184... . - Amiram Eldar, Mar 17 2024
EXAMPLE
L.g.f.: L(x) = 2*x + 8*x^2/2 + 26*x^3/3 + 32*x^4/4 + 62*x^5/5 + 104*x^6/6 +...
where the g.f. of A195584 begins:
exp(L(x)) = 1 + 2*x + 6*x^2 + 18*x^3 + 42*x^4 + 102*x^5 + 238*x^6 +...
MATHEMATICA
Table[DivisorSigma[1, 2n^2]-DivisorSigma[1, n^2], {n, 60}] (* Harvey P. Dale, May 05 2021 *)
PROG
(PARI) {a(n)=sigma(2*n^2)-sigma(n^2)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 20 2011
STATUS
approved