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%I #9 Oct 03 2015 23:53:22
%S 1,1,2,1,3,6,24,12,3,1,4,2,12,6,24,6,30,15,90,45,270,1080,270,135,
%T 1080,360,90,360,60,30,240,120,20,5,20,5,45,90,360,90,720,360,45,90,
%U 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
%N 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.).
%H Harvey P. Dale, <a href="/A140644/b140644.txt">Table of n, a(n) for n = 0..1000</a>
%p 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
%t 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 *)
%Y Cf. A008336.
%K nonn
%O 0,3
%A _Leroy Quet_, Jul 08 2008
%E Extended beyond a(20) by _R. J. Mathar_, Aug 08 2008
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