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
Keywords
Examples
For n = 6, the denominator of Sum_{i=1..6} 1/i is 20 = 2^2*5, so a(7) = 2*5 = 10.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..2370
Programs
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Maple
a:= n-> mul(i[1], i=ifactors(denom(harmonic(n)))[2]): seq(a(n), n=1..33); # Alois P. Heinz, Apr 23 2025
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PARI
a(n) = factorback(factorint(denominator(sum(i=2, n, 1/i)))[, 1]);
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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
Comments