# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a160691 Showing 1-1 of 1 %I A160691 #21 Sep 05 2017 06:10:26 %S A160691 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, %T A160691 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, %U A160691 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 %N A160691 a(n) = the number of divisors of A160689(n) = the number of divisors of A160690(n). %C A160691 From _Farideh Firoozbakht_, May 28 2009: (Start) %C A160691 For the first 200000 natural numbers n, a(n) is in the set {1,2,4,6,8,12} %C A160691 and in fact we have: %C A160691 For one number n, a(n)=1. %C A160691 For 13 numbers n, a(n)=12 (see the sequence A158963). %C A160691 For 4785 numbers n, a(n)=6. %C A160691 For 6706 numbers n, a(n)=8. %C A160691 For 26790 numbers n, a(n)=2. %C A160691 For 161705 numbers n, a(n)=4. %C A160691 Also n=2 is the only number (less than 200000) such that a(n) = a(n+1) = a(n+2) = 2. %C A160691 And for the 53 consecutive numbers 64833, 64834, ..., 64885 we have a(n)=4. (End) %C A160691 a(n)=10 for n=271532 and n=424519 (up to 5*10^5). - _Michel Marcus_, Sep 05 2017 %H A160691 Michel Marcus, Table of n, a(n) for n = 1..5000 %t A160691 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 *) %o A160691 (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 %Y A160691 Cf. A160689, A160690. %Y A160691 Cf. A158963, A158964. [_Farideh Firoozbakht_, May 28 2009] %K A160691 nonn %O A160691 1,2 %A A160691 _Leroy Quet_, May 24 2009 %E A160691 More terms from _Farideh Firoozbakht_, May 28 2009 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE