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A345933 a(n) = n / gcd(n, A002034(n)), where A002034(n) gives the smallest positive integer k such that n divides k!.

%I A345933 #12 Jul 06 2021 18:26:16
%S A345933 1,1,1,1,1,2,1,2,3,2,1,3,1,2,3,8,1,3,1,4,3,2,1,6,5,2,3,4,1,6,1,4,3,2,
%T A345933 5,6,1,2,3,8,1,6,1,4,15,2,1,8,7,5,3,4,1,6,5,8,3,2,1,12,1,2,9,8,5,6,1,
%U A345933 4,3,10,1,12,1,2,15,4,7,6,1,40,9,2,1,12,5,2,3,8,1,15,7,4,3,2,5,12,1,7,9,10,1,6,1,8,15
%N A345933 a(n) = n / gcd(n, A002034(n)), where A002034(n) gives the smallest positive integer k such that n divides k!.
%H A345933 Antti Karttunen, <a href="/A345933/b345933.txt">Table of n, a(n) for n = 1..16384</a>
%H A345933 Antti Karttunen, <a href="/A345933/a345933.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A345933 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A345933 a(n) = n / A345931(n) = n / gcd(n, A002034(n)).
%t A345933 Table[n/GCD[n,m=1;While[Mod[m!,n]!=0,m++];m],{n,100}] (* _Giorgos Kalogeropoulos_, Jul 03 2021 *)
%o A345933 (PARI)
%o A345933 A002034(n) = if(1==n,n,my(s=factor(n)[, 1], k=s[#s], f=Mod(k!, n)); while(f, f*=k++); (k)); \\ After code in A002034.
%o A345933 A345933(n) = (n/gcd(n, A002034(n)));
%Y A345933 Cf. A002034, A345931, A345932.
%K A345933 nonn
%O A345933 1,6
%A A345933 _Antti Karttunen_, Jul 01 2021