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

0,3

Comments

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

Links

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

Formula

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

Example

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.

Prog

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

Crossrefs

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

Sequence in context: A368209 A277809 A051717 * A192441 A108326 A002234

Adjacent sequences: A330027 A330028 A330029 * A330031 A330032 A330033

Keyword

nonn

Author

Jinyuan Wang, Mar 07 2020

Status

approved