A160689 a(1)=1. a(n) = the smallest positive integer such that d(a(n)) = d(Sum_{k=1..n} a(k)), where d(m) = the number of divisors of m.

1, 2, 2, 2, 8, 2, 2, 8, 2, 2, 8, 2, 2, 8, 2, 21, 5, 6, 6, 15, 3, 6, 8, 6, 2, 10, 12, 6, 12, 2, 10, 22, 8, 6, 34, 6, 6, 22, 8, 6, 8, 2, 2, 6, 8, 8, 2, 6, 15, 31, 6, 2, 6, 8, 6, 2, 2, 6, 10, 2, 6, 6, 15, 13, 6, 2, 6, 8, 2, 8, 6, 10, 6, 10, 8, 8, 6, 8, 6, 10, 8, 2, 2, 10, 2, 10, 6, 2, 38, 10, 6, 10, 8, 10, 8

Offset

1,2

Comments

Sum_{k=1..n} a(k) = A160690(n).

d(a(n)) = d(A160690(n)) = A160691(n).

Links

Michel Marcus, Table of n, a(n) for n = 1..5000

Mathematica

a[1] = 1; a[n_] := a[n] = (s = Sum[a[k], {k, n-1}]; For[m = 1, DivisorSigma[0, m] != DivisorSigma[0, s + m], m++]; m); Table[a[n], {n, 95}] (* Farideh Firoozbakht, May 28 2009 *)

Prog

(PARI) lista(nn) = {k = 1; print1(k, ", "); s = k; for (n=2, nn, k = 1; while(numdiv(k) != numdiv(k+s), k++); print1(k, ", "); s += k; ); } \\ Michel Marcus, Sep 04 2017

Crossrefs

Cf. A160690, A160691.

Sequence in context: A087421 A309574 A132697 * A179976 A137508 A055921

Adjacent sequences: A160686 A160687 A160688 * A160690 A160691 A160692

Keyword

nonn

Author

Leroy Quet, May 24 2009

Extensions

More terms from Farideh Firoozbakht, May 28 2009

Status

approved