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A160691 a(n) = the number of divisors of A160689(n) = the number of divisors of A160690(n). 5
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 (list; graph; refs; listen; history; text; internal format)
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: A075016 A279409 A102445 * A049716 A188903 A066671

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

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Last modified November 18 05:25 EST 2017. Contains 294853 sequences.