A116991 a(1)=1. a(n) = number of this sequence's terms a(m), 1<= m <= n-1, each with b(a(m),p) not equal to each b(n,p) for every prime p dividing n, where p^b(k,p) is the highest power of the prime p to divide k.

1, 1, 2, 3, 4, 3, 6, 7, 8, 7, 10, 7, 12, 7, 9, 15, 16, 13, 18, 15, 10, 16, 22, 16, 24, 18, 26, 21, 28, 14, 30, 31, 22, 22, 22, 29, 36, 24, 26, 31, 40, 14, 42, 35, 33, 29, 46, 32, 48, 32, 37, 44, 52, 36, 41, 41, 43, 38, 58, 36, 60, 40, 46, 63, 51, 32, 66, 57, 49, 35, 70, 59, 72

Offset

1,3

Links

Owen Whitby, Table of n, a(n) for n = 1..500

Example

Among the sequence's first 11 terms there are 7 terms that share no common prime-power in their prime-factorization with the prime-powers in the prime-factorization of 12. 12 = 2^2 *3^1. The 7 terms sharing no prime-power with 12 are 1, 1, 2, 7, 8, 7 and 10. The other 4 terms (3, 4, 3 and 6) each share at least one prime-power with 12 in the integers' prime-factorizations.

Mathematica

alist={1}; flist={{{1, 1}}}; Do[a=Length[Select[flist, Intersection[ #, FactorInteger[n]]=={}&]]; AppendTo[alist, a]; AppendTo[flist, FactorInteger[a]], {n, 2, 500}]; Print[alist] - Owen Whitby, May 20 2008

Crossrefs

Sequence in context: A076618 A116550 A283165 * A330061 A330194 A330105

Adjacent sequences: A116988 A116989 A116990 * A116992 A116993 A116994

Keyword

nonn

Author

Leroy Quet, Apr 02 2006

Extensions

More terms from Owen Whitby, May 20 2008

Status

approved