A110412 Sum_{d<n is a divisor of n} tau(n-d).

0, 1, 2, 4, 3, 7, 4, 9, 8, 9, 4, 17, 6, 10, 14, 18, 5, 20, 6, 21, 16, 12, 4, 33, 14, 13, 18, 24, 6, 33, 8, 29, 18, 12, 18, 44, 9, 13, 17, 41, 8, 37, 8, 26, 39, 14, 4, 57, 18, 30, 20, 28, 6, 41, 20, 45, 20, 14, 4, 68, 12, 16, 40, 46, 25, 43, 8, 25, 18, 44, 8, 80, 12, 16, 42, 30, 22, 42, 8

Offset

1,3

Links

Table of n, a(n) for n=1..79.

Formula

It appears that a(n) > tau(n) for n >= 4.

Example

a(9) = tau(9-1)+tau(9-3) = tau(8)+tau(6) = 4+4 = 8.

Maple

with(numtheory): a:=proc(n) local div: div:=divisors(n): sum(tau(n-div[j]), j=1..tau(n)-1): end: seq(a(n), n=2..90); # Emeric Deutsch, Aug 05 2005

Mathematica

f[n_] := Plus @@ (DivisorSigma[0, n - # ] & /@ Most[Divisors[n]]); Table[ f[n], {n, 79}] (* Robert G. Wilson v, Aug 05 2005 *)

Prog

(PARI) a(n) = sumdiv(n, d, if (d<n, numdiv(n-d))); \\ Michel Marcus, Aug 20 2019

Crossrefs

Cf. A007425.

Sequence in context: A181049 A007203 A354707 * A266285 A258851 A194031

Adjacent sequences: A110409 A110410 A110411 * A110413 A110414 A110415

Keyword

nonn

Author

Amarnath Murthy, Jul 31 2005

Extensions

Edited, corrected and extended by Emeric Deutsch and Robert G. Wilson v, Aug 05 2005

Status

approved