A227733 a(n) = sigma(2*n)^2 - sigma(n)^2.

8, 40, 128, 176, 288, 640, 512, 736, 1352, 1440, 1152, 2816, 1568, 2560, 4608, 3008, 2592, 6760, 3200, 6336, 8192, 5760, 4608, 11776, 7688, 7840, 12800, 11264, 7200, 23040, 8192, 12160, 18432, 12960, 18432, 29744, 11552, 16000, 25088, 26496, 14112, 40960, 15488, 25344, 48672, 23040

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

Cf. A000203, A002117, A227732.

Sequence in context: A135796 A105374 A162668 * A191903 A028596 A264602

Adjacent sequences: A227730 A227731 A227732 * A227734 A227735 A227736

Keyword

nonn

Author

Paul D. Hanna, Jul 24 2013

Status

approved