A072379 Sum_{k<=n} (sigma(k)^2), where sigma(k) denotes the sum of the divisors of k A000203.

1, 10, 26, 75, 111, 255, 319, 544, 713, 1037, 1181, 1965, 2161, 2737, 3313, 4274, 4598, 6119, 6519, 8283, 9307, 10603, 11179, 14779, 15740, 17504, 19104, 22240, 23140, 28324, 29348, 33317, 35621, 38537, 40841, 49122, 50566, 54166, 57302

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Formula

Ramanujan's asymptotic formula: (5/6)*Zeta(3)*n^3+O(n^2*log(n)^2)

Maple

A072379 := proc(n)
    add( numtheory[sigma](k)^2, k=0..n) ;
end proc:
seq(A072379(n), n=1..80) ; # R. J. Mathar, Jul 09 2024

Mathematica

Accumulate[Table[DivisorSigma[1, k]^2, {k, 1, 50}]] (* Vaclav Kotesovec, Sep 10 2018 *)

Prog

(PARI) a(n) = sum(k=1, n, sigma(k)^2) \\ Michel Marcus, Jun 20 2013

Crossrefs

Cf. A024916, A072861.

Cf. A057434, A061502, A074789.

Sequence in context: A134420 A144255 A259290 * A005970 A192254 A368502

Adjacent sequences: A072376 A072377 A072378 * A072380 A072381 A072382

Keyword

nonn

Author

Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 20 2002

Status

approved