A140644 a(0)=1. a(n) = a(n-1)/d(n) if d(n) divides a(n-1). Otherwise, a(n) = a(n-1)*d(n). (d(n) is the number of positive divisors of n.).

1, 1, 2, 1, 3, 6, 24, 12, 3, 1, 4, 2, 12, 6, 24, 6, 30, 15, 90, 45, 270, 1080, 270, 135, 1080, 360, 90, 360, 60, 30, 240, 120, 20, 5, 20, 5, 45, 90, 360, 90, 720, 360, 45, 90, 15, 90, 360, 180, 18, 6, 1, 4, 24, 12, 96, 24, 3, 12, 3, 6, 72, 36, 9, 54, 378, 1512, 189, 378, 63

Offset: 0

Author

Leroy Quet, Jul 08 2008

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A008336.

Programs

Maple

A140644 := proc(n) option remember ; local d ; if n = 0 then 1; else d := numtheory[tau](n) ; if A140644(n-1) mod d = 0 then RETURN( A140644(n-1)/d ) ; else RETURN( d*A140644(n-1) ) ; fi; fi; end: for n from 0 to 80 do printf("%d,",A140644(n)) ; od: # R. J. Mathar, Aug 08 2008

Mathematica

nxt[{n_,a_}]:=Module[{d=DivisorSigma[0,n+1]},{n+1,If[Divisible[a,d], a/d, a*d]}]; Transpose[NestList[nxt,{0,1},70]][[2]] (* Harvey P. Dale, Jul 25 2015 *)

Extensions

Extended beyond a(20) by R. J. Mathar, Aug 08 2008