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A346088 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.

%I A346088 #10 Jul 09 2021 22:15:47
%S A346088 1,2,3,4,5,3,7,4,9,5,11,4,13,7,5,16,17,9,19,5,7,11,23,4,25,13,27,7,29,
%T A346088 5,31,32,11,17,7,9,37,19,13,5,41,7,43,11,9,23,47,16,49,25,17,13,53,27,
%U A346088 11,7,19,29,59,5,61,31,7,32,13,11,67,17,23,7,71,9,73,37,25,19,11,13,79,16,27,41,83,7,17,43,29,11,89
%N A346088 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 A346088 Antti Karttunen, <a href="/A346088/b346088.txt">Table of n, a(n) for n = 1..20000</a>
%F A346088 a(n) = n / A346089(n).
%e A346088 36 has 9 divisors: 1, 2, 3, 4, 6, 9, 12, 18, 36. When A002034 is applied to them, one obtains values [1, 2, 3, 4, 3, 6, 4, 6, 6], thus there are three divisors that obtain the maximal value 6 obtained at 36 itself, of which divisor 9 is the smallest, and therefore a(36) = 9.
%o A346088 (PARI)
%o A346088 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 A346088 A346088(n) = { my(x=A002034(n)); fordiv(n,d,if(A002034(d)==x, return(d))); };
%Y A346088 Cf. A002034, A345935, A345936, A346089.
%Y A346088 Cf. also A344758.
%Y A346088 Differs from A223491 for the first time at n=27, where a(27) = 27, while A223491(27) = 9.
%K A346088 nonn
%O A346088 1,2
%A A346088 _Antti Karttunen_, Jul 05 2021