A195585 sigma(2*n^2) - sigma(n^2).

2, 8, 26, 32, 62, 104, 114, 128, 242, 248, 266, 416, 366, 456, 806, 512, 614, 968, 762, 992, 1482, 1064, 1106, 1664, 1562, 1464, 2186, 1824, 1742, 3224, 1986, 2048, 3458, 2456, 3534, 3872, 2814, 3048, 4758, 3968, 3446, 5928, 3786, 4256, 7502, 4424, 4514, 6656, 5602, 6248, 7982

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

Cf. A195584, A215603, A054785, A015128, A002117.

Sequence in context: A150672 A150673 A242747 * A102942 A212691 A206803

Adjacent sequences: A195582 A195583 A195584 * A195586 A195587 A195588

Keyword

nonn

Author

Paul D. Hanna, Sep 20 2011

Status

approved