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a(1) = 1, a(n) = number of divisors of n*a(n-1).
4

%I #11 Nov 17 2024 11:28:44

%S 1,2,4,5,3,6,8,7,6,12,12,15,8,10,12,14,8,15,8,12,18,18,12,18,18,18,12,

%T 20,12,24,16,10,16,12,24,24,16,12,18,30,16,24,16,14,24,20,12,21,8,15,

%U 12,20,12,20,18,30,24,20,12,30,16,12,24,20,18,24,16,14,16,24,16,24,16,12

%N a(1) = 1, a(n) = number of divisors of n*a(n-1).

%C a(n)=A000005(n*a(n-1)) for n>1, a(1)=1;

%C see A119792 and A119793 for record values and where they occur: A119792(n)=a(A119793(n)).

%H Ivan Neretin, <a href="/A119791/b119791.txt">Table of n, a(n) for n = 1..10000</a>

%t Fold[Append[#1, DivisorSigma[0, #1[[-1]]*#2]] &, {1}, Range[2, 74]] (* _Ivan Neretin_, Sep 01 2016 *)

%t nxt[{n_,a_}]:={n+1,DivisorSigma[0,a(n+1)]}; NestList[nxt,{1,1},80][[;;,2]] (* _Harvey P. Dale_, Nov 16 2024 *)

%K nonn,changed

%O 1,2

%A _Reinhard Zumkeller_, May 24 2006