A102128 a(1) = 1; a(n) = sum of previous terms which divide n.

1, 1, 2, 4, 2, 6, 2, 12, 2, 10, 2, 34, 2, 14, 2, 20, 2, 24, 2, 54, 2, 22, 2, 70, 2, 26, 2, 46, 2, 46, 2, 36, 2, 68, 2, 94, 2, 38, 2, 74, 2, 62, 2, 70, 2, 138, 2, 94, 2, 60, 2, 82, 2, 114, 2, 74, 2, 58, 2, 172, 2, 124, 2, 68, 2, 94, 2, 242, 2, 234, 2, 154, 2, 222, 2, 118, 2, 110, 2, 114, 2

Offset: 1

Author

Leroy Quet, Feb 14 2005

Keywords

• nonn

Examples

			Among the first 7 terms, the terms which divide 8 are 1, 1, 2, 4, 2 and 2.
So a(8) = 1 + 1 + 2 + 4 + 2 + 2 = 12.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A088167.

Programs

Mathematica

Nest[Function[{a, n}, Append[a, Total@ Select[a, Mod[n, #] == 0 &]]] @@ {#, Length@ # + 1} &, {1}, 80] (* Michael De Vlieger, Nov 13 2018 *)

PARI

up_to = 20000;
A102128list(up_to) = { my(v=vector(up_to)); v[1] = 1; for(n=2,up_to,v[n] = sum(j=1,n-1,v[j]*!(n%v[j]))); (v); };
v102128 = A102128list(up_to);
A102128(n) = v102128[n]; \\ Antti Karttunen, Nov 10 2018

Formula

a(1) = 1; a(n) = [x^n] Sum_{k=1..n-1} a(k)*x^a(k)/(1 - x^a(k)). - Ilya Gutkovskiy, Dec 11 2017

Extensions

More terms from John W. Layman, Mar 16 2005