A069546 a(n) = Sum_{d|n} sigma(n*d).

1, 10, 17, 53, 37, 170, 65, 236, 174, 370, 145, 901, 197, 650, 629, 987, 325, 1740, 401, 1961, 1105, 1450, 577, 4012, 968, 1970, 1618, 3445, 901, 6290, 1025, 4026, 2465, 3250, 2405, 9222, 1445, 4010, 3349, 8732, 1765, 11050, 1937, 7685, 6438, 5770

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p^e) = (p^(e+1)*(p^(e+1)-1)-(p-1)*(e+1))/(p-1)^2.

Sum_{k=1..n} a(k) ~ c * n^3, where c = ((zeta(2)*zeta(3)^2)/3) * Product_{p prime} (1 + 1/p^2 - 1/p^4 - 1/p^5) = 1.09461730308... . - Amiram Eldar, Oct 28 2022

Mathematica

Table[ Apply[ Plus, DivisorSigma[1, n*Divisors[n]]], {n, 1, 50}]
f[p_, e_] := (p^(e + 1)*(p^(e + 1) - 1) - (p - 1)*(e + 1))/(p - 1)^2; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Oct 28 2022 *)

Prog

(Magma) [&+[DivisorSigma(1, n*d):d in Divisors(n)]:n in [1..50]]; // Marius A. Burtea, Sep 15 2019
(PARI) a(n) = sumdiv(n, d, sigma(n*d)); \\ Michel Marcus, Sep 15 2019

Crossrefs

Cf. A061391, A062354.

Cf. A002117, A013661.

Sequence in context: A164285 A268183 A293690 * A065018 A039336 A043159

Adjacent sequences: A069543 A069544 A069545 * A069547 A069548 A069549

Keyword

mult,easy,nonn

Author

Vladeta Jovovic, Apr 17 2002

Extensions

Edited and extended by Robert G. Wilson v, Apr 22 2002

Status

approved