OFFSET
2,1
COMMENTS
If n^3 is written in different number bases, a(n) is an upper limit for the count of number bases which allow n^3 to be written as a base-b number with a digit sum of n (generalized Dudeney numbers).
a(n) has an upper limit in the number of divisors of n^3-n. Let d be one of these divisors, then it appears that a lower limit can be found by excluding all divisors d where d+1 does not share all its prime divisors with binomial(n^3, n) (A107444).
FORMULA
EXAMPLE
a(2) = 3 because 2^3 = 2^2 + 2^2 = 4^1 + 4^1 = 7^1 + 7^0.
PROG
(PARI) a(n) = sum(d=2, n^3, s=sumdigits(n^3, d); s<=n&&(n-s)%(d-1)==0); \\ Jinyuan Wang, Jan 15 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Scheuerle, Jan 12 2022
EXTENSIONS
More terms from Jinyuan Wang, Jan 15 2022
STATUS
approved