A330030 Least k such that Sum_{i=0..n} k^n / i! is a positive integer.

1, 1, 2, 3, 6, 30, 30, 42, 210, 42, 210, 2310, 2310, 30030, 30030, 30030, 30030, 39270, 510510, 1939938, 9699690, 9699690, 9699690, 17160990, 223092870, 903210, 223092870, 223092870, 223092870, 6469693230, 6469693230, 200560490130, 200560490130, 10555815270, 200560490130

Offset: 0

Author

Jinyuan Wang, Mar 07 2020

Keywords

• nonn

Comments

Least k > 0 such that k^n/A061355(n) is an integer.

Examples

			For n = 7, the denominator of Sum_{i=0..7} 1/i! is 252 = 2^2*3^2*7, so a(7) = 2*3*7 = 42.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A000142, A007947, A061354, A061355, A332734, A333196.

Programs

PARI

a(n) = factorback(factorint(denominator(sum(i=2, n, 1/i!)))[, 1]);

Formula

a(n) = A007947(A061355(n)).