A067951 a(0) = 1; a(n) = Sum_{1 <= k <= n and k|n} a(n-k).

1, 1, 2, 3, 6, 7, 17, 18, 42, 60, 110, 111, 341, 342, 702, 1154, 2240, 2241, 6037, 6038, 15580, 22320, 38012, 38013, 122544, 138125, 261012, 389594, 796173, 796174, 2259345, 2259346, 5439649, 7737007, 13178898, 16234417, 45367492, 45367493

Offset: 0

Author

Naohiro Nomoto, Mar 07 2002

Keywords

• easy
• nonn

Comments

With offset 1, eigensequence of triangle A113998. - Gary W. Adamson, Sep 12 2016

a(n) = a(n-1)+1 iff n is prime. - Robert Israel, Sep 13 2016

Links

• Robert Israel, Table of n, a(n) for n = 0..4680

Crossrefs

Cf. A113998.

Programs

Maple

f:=proc(n) option remember;
   add(procname(n-k), k=numtheory:-divisors(n))
end proc:
f(0):= 1:
seq(f(n),n=0..50); # Robert Israel, Sep 13 2016

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[a[n - k], {k, Divisors@ n}]; Table[a@ n, {n, 0, 37}] (* Michael De Vlieger, Sep 13 2016 *)

PARI

a(n)=if (n==0, return(1)); my(an = 0); fordiv(n, k, an += a(n-k)); an; \\ Michel Marcus, Jul 14 2013