

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
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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



