%I #9 Jul 09 2021 22:16:05
%S 1,1,1,1,1,2,1,2,1,2,1,3,1,2,3,1,1,2,1,4,3,2,1,6,1,2,1,4,1,6,1,1,3,2,
%T 5,4,1,2,3,8,1,6,1,4,5,2,1,3,1,2,3,4,1,2,5,8,3,2,1,12,1,2,9,2,5,6,1,4,
%U 3,10,1,8,1,2,3,4,7,6,1,5,3,2,1,12,5,2,3,8,1,10,7,4,3,2,5,3,1,2,9,4,1,6,1,8,15
%N a(n) = n divided by the smallest divisor d of n for which A002034(d) = A002034(n), where A002034(n) is the smallest positive integer k such that k! is a multiple of n.
%H Antti Karttunen, <a href="/A346089/b346089.txt">Table of n, a(n) for n = 1..16384</a>
%H Antti Karttunen, <a href="/A346089/a346089.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F a(n) = n / A346088(n).
%o (PARI)
%o 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 A346089(n) = { my(x=A002034(n)); fordiv(n,d,if(A002034(d)==x, return(n/d))); };
%Y Cf. A002034, A345935, A345936, A345944 (positions of 1's), A346088.
%Y Cf. also A344759.
%Y Differs from A302776 for the first time at n=27, where a(27) = 1, while A302776(27) = 3.
%K nonn
%O 1,6
%A _Antti Karttunen_, Jul 05 2021