A068342 a(1) = 1; a(n+1) = (product{k|n} a(k)) (sum{j|n} 1/a(j)), where both the product and sum are over the positive divisors of n.

1, 1, 2, 3, 7, 8, 42, 43, 304, 914, 13717, 13718, 1948004, 1948005, 165580467, 3808350755, 1157738629649, 1157738629650, 14800530641450464, 14800530641450465, 703750431470328179479, 90080055228202006973396, 2471346315185722061315132977

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..68

Example

a(7) = a(1) a(2) a(3) a(6) (1/a(1) + 1/a(2) + 1/a(3) + 1/a(6)) = 1 *1 *2 *8 *(1 + 1 + 1/2 + 1/8) = 42.

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n=1, 1, (l->
      mul(a(i), i=l)*add(1/a(i), i=l))(divisors(n-1)))
    end:
seq(a(n), n=1..25);  # Alois P. Heinz, May 22 2015

Mathematica

a[1] = 1;
a[n_] := a[n] = With[{k = a /@ Divisors[n-1]}, (Times @@ k)*Total[1/k]];
Array[a, 25] (* Jean-François Alcover, Mar 28 2017 *)

Crossrefs

Sequence in context: A056433 A288628 A064669 * A038034 A103173 A378270

Adjacent sequences: A068339 A068340 A068341 * A068343 A068344 A068345

Keyword

nonn

Author

Leroy Quet, Feb 27 2002

Status

approved