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a(n) = a(n-1)* d(n) if gcd(n,a(n-1))=1, otherwise a(n) = a(n-1)/gcd(n,a(n-1)). Here gcd(n,a(n-1)) is greatest common divisor, d(n) is number of divisors.
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%I #18 Dec 29 2023 10:50:34

%S 1,1,2,4,1,2,1,2,1,3,12,24,2,4,2,8,1,2,1,2,1,4,2,4,1,3,12,4,1,2,1,2,1,

%T 4,2,8,2,4,2,8,1,2,1,2,1,6,3,6,1,3,18,6,3,6,1,4,1,4,2,4,1,2,1,6,3,12,

%U 2,4,1,4,2,4,1,2,1,6,3,12,2,4,1,5,20,40,10,2,1,4,1,2,1,4,1,4,2,8

%N a(n) = a(n-1)* d(n) if gcd(n,a(n-1))=1, otherwise a(n) = a(n-1)/gcd(n,a(n-1)). Here gcd(n,a(n-1)) is greatest common divisor, d(n) is number of divisors.

%H Robert Israel, <a href="/A133902/b133902.txt">Table of n, a(n) for n = 0..10000</a>

%p A[0]:= 1:

%p for n from 1 to 1000 do

%p g:= igcd(n,A[n-1]);

%p if g = 1 then A[n]:= A[n-1]*numtheory:-tau(n) else A[n]:= A[n-1]/g fi

%p od:

%p seq(A[i],i=0..1000); # _Robert Israel_, Aug 10 2020

%t Nest[Append[#1, If[#3 == 1, Last[#1]*DivisorSigma[0, #2], Last[#1]/#3]] & @@ {#1, #2, GCD[Last[#1], #2]} & @@ {#, Length[#] + 1} &, {1, 1}, 93] (* _Michael De Vlieger_, Mar 21 2022 *)

%Y Cf. A000005, A034444, A001222.

%K nonn

%O 0,3

%A _Ctibor O. Zizka_, Jan 07 2008

%E Corrected, extended and offset changed by _Robert Israel_, Aug 10 2020