A333196 Least k such that Sum_{i=1..n} k^n / i is a positive integer.

1, 2, 6, 6, 30, 10, 70, 70, 210, 210, 2310, 2310, 30030, 30030, 30030, 30030, 510510, 510510, 9699690, 1939938, 646646, 646646, 14872858, 44618574, 223092870, 223092870, 223092870, 223092870, 6469693230, 6469693230, 200560490130, 200560490130, 18232771830

Offset

1,2

Comments

Least k > 0 such that k^n/A002805(n) is an integer.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..2370

Formula

a(n) = A007947(A002805(n)).

Example

For n = 6, the denominator of Sum_{i=1..6} 1/i is 20 = 2^2*5, so a(7) = 2*5 = 10.

Prog

(PARI) a(n) = factorback(factorint(denominator(sum(i=2, n, 1/i)))[, 1]);
(Python)
from functools import reduce
from operator import mul
from sympy import harmonic, factorint
def A333196(n):
    fs = factorint(harmonic(n).q)
    return 1 if len(fs) == 0 else reduce(mul, (p**(fs[p]//n + 1 if fs[p] % n else fs[p]//n) for p in fs)) # Chai Wah Wu, Apr 03 2020

Crossrefs

Cf. A007947, A001008, A002805, A330030, A333072.

Sequence in context: A366369 A163641 A333072 * A216850 A070889 A072744

Adjacent sequences: A333193 A333194 A333195 * A333197 A333198 A333199

Keyword

nonn

Author

Jinyuan Wang, Mar 10 2020

Status

approved