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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jul 05 2021

Keywords

• nonn

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A002034, A345935, A345936, A346089.

Cf. also A344758.

Differs from A223491 for the first time at n=27, where a(27) = 27, while A223491(27) = 9.

Programs

PARI

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.
A346088(n) = { my(x=A002034(n)); fordiv(n,d,if(A002034(d)==x, return(d))); };

Formula

a(n) = n / A346089(n).