OFFSET
0,2
COMMENTS
LINKS
Amiram Eldar, Table of n, a(n) for n = 0..2109 (terms below 10^7)
Paul Erdős, Miscellaneous problems in number theory, Proceedings of the Eleventh Manitoba Conference on Numerical Mathematics and Computing (Winnipeg, Man., 1981), Congr. Numer., Vol. 34 (1982), pp. 25-45.
EXAMPLE
a(1) = 2 since 2! = 2^1 is the least factorial with a single exponent (1) in its prime factorization.
a(2) = 4 since 4! = 24 = 2^3 * 3^1 is the least factorial with 2 distinct exponents (1 and 3) in its prime factorization.
a(3) = 6 since 6! = 720 = 2^4 * 3^2 * 5^1 is the least factorial with 3 distinct exponents (1, 2 and 4) in its prime factorization.
MATHEMATICA
f[1] = 0; f[n_] := Length @ Union[FactorInteger[n!][[;; , 2]]]; seq[max_] := Module[{s = Table[0, {max}], n = 1, c = 0}, While[c < max, i = f[n] + 1; If[i <= max && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[50]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 27 2021
STATUS
approved