OFFSET
1,1
COMMENTS
Here sigma(n) is the sum of divisors of n (A000203).
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..1000
FORMULA
Logarithmic derivative of A227732.
Sum_{k=1..n} a(k) ~ c * n^3, where c = (49/12) * zeta(3) = 4.908399021235... . - Amiram Eldar, Mar 17 2024
EXAMPLE
L.g.f.: L(x) = 8*x + 40*x^2/2 + 128*x^3/3 + 176*x^4/4 + 288*x^5/5 + 640*x^6/6 +...
where
exp(L(x)) = 1 + 8*x + 52*x^2 + 288*x^3 + 1396*x^4 + 6208*x^5 + 25744*x^6 +...+ A227732(n)*x^n +...
MATHEMATICA
a[n_] := DivisorSigma[1, 2*n]^2 - DivisorSigma[1, n]^2; Array[a, 50] (* Amiram Eldar, Mar 17 2024 *)
PROG
(PARI) {a(n)=sigma(2*n)^2-sigma(n)^2}
for(n=1, 50, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 24 2013
STATUS
approved