cp's OEIS Frontend

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

%I A333196 #11 Apr 23 2025 19:40:30
%S A333196 1,2,6,6,30,10,70,70,210,210,2310,2310,30030,30030,30030,30030,510510,
%T A333196 510510,9699690,1939938,646646,646646,14872858,44618574,223092870,
%U A333196 223092870,223092870,223092870,6469693230,6469693230,200560490130,200560490130,18232771830
%N A333196 Least k such that Sum_{i=1..n} k^n / i is a positive integer.
%C A333196 Least k > 0 such that k^n/A002805(n) is an integer.
%H A333196 Chai Wah Wu, <a href="/A333196/b333196.txt">Table of n, a(n) for n = 1..2370</a>
%F A333196 a(n) = A007947(A002805(n)).
%e A333196 For n = 6, the denominator of Sum_{i=1..6} 1/i is 20 = 2^2*5, so a(7) = 2*5 = 10.
%p A333196 a:= n-> mul(i[1], i=ifactors(denom(harmonic(n)))[2]):
%p A333196 seq(a(n), n=1..33);  # _Alois P. Heinz_, Apr 23 2025
%o A333196 (PARI) a(n) = factorback(factorint(denominator(sum(i=2, n, 1/i)))[, 1]);
%o A333196 (Python)
%o A333196 from functools import reduce
%o A333196 from operator import mul
%o A333196 from sympy import harmonic, factorint
%o A333196 def A333196(n):
%o A333196     fs = factorint(harmonic(n).q)
%o A333196     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
%Y A333196 Cf. A007947, A001008, A002805, A330030, A333072.
%K A333196 nonn
%O A333196 1,2
%A A333196 _Jinyuan Wang_, Mar 10 2020