A118291 a(1) = 1. a(n) = number of terms among the sequence's first (n-1) terms which are divisible by the largest prime dividing a(n-1), or which are divisible by 1 if a(n-1)= 1.

1, 1, 2, 1, 4, 2, 3, 1, 8, 4, 5, 1, 12, 2, 7, 1, 16, 8, 9, 3, 4, 10, 2, 12, 5, 3, 6, 7, 2, 15, 4, 16, 17, 1, 34, 2, 19, 1, 38, 2, 21, 3, 10, 5, 6, 11, 1, 47, 1, 49, 4, 24, 12, 13, 1, 55, 2, 27, 14, 5, 8, 29, 1, 63, 6, 16, 31, 1, 68, 3, 17, 4, 33, 3, 19, 3, 20, 9, 21, 7, 8, 35, 9, 23, 1, 85, 5, 12

Offset

1,3

Comments

If a(n-1) = 1, then a(n) = n-1, obviously.

Links

Table of n, a(n) for n=1..88.

Example

a(13)= 12. So a(14) = the number of terms among the first 13 terms which are divisible by the largest prime dividing 12 (which is 3).
a(7)=3 and a(13) = 12 are the two terms each divisible by 3, so a(14) = 2.

Maple

A006530 := proc(n) local ifs, i ; if n <= 3 then n ; else ifs := ifactors(n)[2] ; max( seq(op(1, i), i=ifs)) ; fi ; end: A118291 := proc(n) local a, anxt, i ; a := [1, 1] ; while nops(a) < n do anxt := 0 ; for i in a do if i mod A006530(op(-1, a)) = 0 then anxt := anxt+1 ; fi ; od: a := [op(a), anxt] ; od; a ; end: A118291(200) ; # R. J. Mathar, Sep 06 2007

Crossrefs

Cf. A118290.

Sequence in context: A128520 A269370 A123755 * A118290 A131271 A208569

Adjacent sequences: A118288 A118289 A118290 * A118292 A118293 A118294

Keyword

nonn

Author

Leroy Quet, Apr 22 2006

Extensions

More terms from R. J. Mathar, Sep 06 2007

Status

approved