A065805 a(n) = Sum_{j=0..n} sigma_j(n).

2, 10, 44, 377, 3912, 57214, 960808, 19261862, 435877584, 11123320200, 313842837684, 9729290348250, 328114698808288, 11967567841654610, 469172063576559648, 19676848703371278527, 878942778254232811956, 41661071646298278566892, 2088331858752553232964220

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..386 (terms 1..100 from Harry J. Smith)

Formula

a(n) ~ n^(n+1) / (n-1). - Vaclav Kotesovec, Sep 11 2018

a(n) = n + 1 + Sum_{d|n, d<n} (d^(n+1) - 1)/(d - 1). - Amiram Eldar, Mar 02 2025

Example

For n = 6, a(6) = 4 + 12 + 50 + 252 + 1394 + 8052 + 47450 = 57214.

Mathematica

a[n_] := Apply[Plus, Table[DivisorSigma[w, n], {w, 0, n}]]; Array[a, 30]
a[n_] := DivisorSum[n, (#^(n + 1) - 1)/(# - 1) &, # > 1 &] + n + 1; Array[a, 30] (* Amiram Eldar, Mar 01 2025 *)

Prog

(PARI) a(n) = sum(j=0, n, sigma(n, j)); \\ Harry J. Smith, Oct 31 2009
(PARI) a(n) = sumdiv(n, d, if(d == 1, n+1, (d^(n+1) - 1)/(d - 1))); \\ Amiram Eldar, Mar 01 2025

Crossrefs

Cf. A000005, A000203, A001157, A319194.

Sequence in context: A142983 A227852 A347524 * A145239 A068561 A068484

Adjacent sequences: A065802 A065803 A065804 * A065806 A065807 A065808

Keyword

nonn,changed

Author

Labos Elemer, Nov 21 2001

Status

approved