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A102128 a(1) = 1; a(n) = sum of previous terms which divide n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

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

EXAMPLE

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.

MATHEMATICA

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

PROG

(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

CROSSREFS

Cf. A088167.

Sequence in context: A213372 A286601 A340071 * A181980 A230436 A105393

Adjacent sequences:  A102125 A102126 A102127 * A102129 A102130 A102131

KEYWORD

nonn

AUTHOR

Leroy Quet, Feb 14 2005

EXTENSIONS

More terms from John W. Layman, Mar 16 2005

STATUS

approved

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Last modified March 7 19:13 EST 2021. Contains 341928 sequences. (Running on oeis4.)