A333072 Least k such that Sum_{i=1..n} k^i / i is a positive integer.
1, 2, 6, 6, 30, 10, 70, 70, 210, 168, 1848, 1848, 18018, 8580, 2574, 2574, 102102, 102102, 831402, 2771340, 3233230, 587860, 43266496, 117630786, 162249360, 145088370, 145088370, 2897310, 672175920, 672175920, 18232771830, 18232771830, 44279588730, 8886561060
Offset: 1
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..61
Programs
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PARI
a(n) = {my(m = prod(i=primepi(n/2)+1, primepi(n), prime(i)), k = m); while (denominator(sum(i=2, n, k^i/i)) != 1, k += m); k; } -
Python
from sympy import primorial, lcm def A333072(n): f = 1 for i in range(1,n+1): f = lcm(f,i) f, glist = int(f), [] for i in range(1,n+1): glist.append(f//i) m = 1 if n < 2 else primorial(n,nth=False)//primorial(n//2,nth=False) k = m while True: p,ki = 0, k for i in range(1,n+1): p = (p+ki*glist[i-1]) % f ki = (k*ki) % f if p == 0: return k k += m # Chai Wah Wu, Apr 04 2020
Formula
a(n) <= A034386(n).
Comments