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

1,2

Links

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

Formula

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

Example

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.

Prog

(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))); };

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.

Sequence in context: A353172 A140271 A223491 * A275823 A141295 A134198

Adjacent sequences: A346085 A346086 A346087 * A346089 A346090 A346091

Keyword

nonn

Author

Antti Karttunen, Jul 05 2021

Status

approved