A160691 a(n) = the number of divisors of A160689(n) = the number of divisors of A160690(n).

1, 2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 4, 2, 4, 4, 4, 2, 4, 4, 4, 2, 4, 6, 4, 6, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 2, 4, 4, 2, 4, 2, 4, 4, 4, 2, 2, 4, 4, 2, 4, 4, 4, 2, 4, 2, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 2, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 2, 4, 4, 2, 4, 4, 2

Offset

1,2

Comments

From Farideh Firoozbakht, May 28 2009: (Start)

For the first 200000 natural numbers n, a(n) is in the set {1,2,4,6,8,12}

and in fact we have:

For one number n, a(n)=1.

For 13 numbers n, a(n)=12 (see the sequence A158963).

For 4785 numbers n, a(n)=6.

For 6706 numbers n, a(n)=8.

For 26790 numbers n, a(n)=2.

For 161705 numbers n, a(n)=4.

Also n=2 is the only number (less than 200000) such that a(n) = a(n+1) = a(n+2) = 2.

And for the 53 consecutive numbers 64833, 64834, ..., 64885 we have a(n)=4. (End)

a(n)=10 for n=271532 and n=424519 (up to 5*10^5). - Michel Marcus, Sep 05 2017

Links

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

Mathematica

c[1] = 1; c[n_] := c[n] = (s = Sum[c[k], {k, n - 1}]; For[m = 1, DivisorSigma[0, m] != DivisorSigma[0, s + m], m++]; m); a[n_] := a[n] = DivisorSigma[0, c[n]]; Table[a[n], {n, 105}] (* Farideh Firoozbakht, May 28 2009 *)

Prog

(PARI) lista(nn) = {k = 1; print1(numdiv(k), ", "); last = k; for (n=2, nn, k = last+1; while(numdiv(k) != numdiv(k - last), k++); print1(numdiv(k), ", "); s += k; last = k; ); } \\ Michel Marcus, Sep 05 2017

Crossrefs

Cf. A160689, A160690.

Cf. A158963, A158964. [Farideh Firoozbakht, May 28 2009]

Sequence in context: A279409 A102445 A102430 * A367626 A049716 A361289

Adjacent sequences: A160688 A160689 A160690 * A160692 A160693 A160694

Keyword

nonn

Author

Leroy Quet, May 24 2009

Extensions

More terms from Farideh Firoozbakht, May 28 2009

Status

approved