OFFSET
1,3
COMMENTS
For each prime p >= 2, the exponent of p in a(n) is the largest integer t such that p^t is less than or equal to the sum of digits of n in base p.
n!*a(n) is the smallest common denominator of the n-th degree coefficients of the Baker-Campbell-Hausdorff series.
LINKS
Harald Hofstätter, Table of n, a(n) for n = 1..20000
Harald Hofstätter, Denominators of coefficients of the Baker-Campbell-Hausdorff series, arXiv:2010.03440 [math.NT], 2020.
Harald Hofstätter, Smallest common denominators for the homogeneous components of the Baker-Campbell-Hausdorff series, arXiv:2012.03818 [math.NT], 2020.
Harald Hofstätter, A simple and efficient algorithm for computing the Baker-Campbell-Hausdorff series, arXiv:2212.01290 [math.RA], 2022.
Eric Weisstein's World of Mathematics, Baker-Campbell-Hausdorff Series.
MAPLE
PROG
(Julia)
using Primes
A338025(n::Int) =
prod([p^(floor(Int, log(p, sum(digits(n, base=p)))))
for p in 2:n if isprime(p)])
println([A338025(n) for n = 1:50])
(PARI) a(n) = {my(v = matrix(primepi(n), 2, i, j, my(p=prime(i)); if (j==1, p, logint(sumdigits(n, p), p)))); factorback(v); } \\ Michel Marcus, Oct 08 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Harald Hofstätter, Oct 07 2020
STATUS
approved