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A345931 a(n) = gcd(n, A002034(n)), where A002034(n) gives the smallest positive integer k such that n divides k!.

%I A345931 #13 Jul 06 2021 18:28:30
%S A345931 1,2,3,4,5,3,7,4,3,5,11,4,13,7,5,2,17,6,19,5,7,11,23,4,5,13,9,7,29,5,
%T A345931 31,8,11,17,7,6,37,19,13,5,41,7,43,11,3,23,47,6,7,10,17,13,53,9,11,7,
%U A345931 19,29,59,5,61,31,7,8,13,11,67,17,23,7,71,6,73,37,5,19,11,13,79,2,9,41,83,7,17,43,29,11,89
%N A345931 a(n) = gcd(n, A002034(n)), where A002034(n) gives the smallest positive integer k such that n divides k!.
%H A345931 Antti Karttunen, <a href="/A345931/b345931.txt">Table of n, a(n) for n = 1..20000</a>
%H A345931 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A345931 a(n) = gcd(n, A002034(n)) = gcd(n, A072480(n)) = gcd(A002034(n), A072480(n)).
%F A345931 a(n) = A002034(n) / A345932(n).
%F A345931 a(n) = n / A345933(n).
%t A345931 Table[GCD[n,m=1;While[Mod[m!,n]!=0,m++];m],{n,100}] (* _Giorgos Kalogeropoulos_, Jul 02 2021 *)
%o A345931 (PARI)
%o A345931 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 A345931 A345931(n) = gcd(n, A002034(n));
%Y A345931 Cf. A002034, A072480, A345932, A345933.
%K A345931 nonn
%O A345931 1,2
%A A345931 _Antti Karttunen_, Jul 01 2021