OFFSET
1,1
COMMENTS
The sequence is connected with a 1980-Erdős-Graham conjecture that, for every N, there exists an n such that in prime power factorization of n! at least N first exponents are even. In 1997, this conjecture was proved by D. Berend. A generalization was given by Y.-G. Chen (2003).
REFERENCES
P. Erdős, P. L. Graham, Old and new problems and results in combinatorial number theory, L'Enseignement Mathematique, Imprimerie Kunding, Geneva, 1980.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..46 (first 36 terms from Hiroaki Yamanouchi)
D. Berend, Parity of exponents in the factorization of n!, J. Number Theory, 64 (1997), 13-19.
Y.-G. Chen, On the parity of exponents in the standard factorization of n!, J. Number Theory, 100 (2003), 326-331.
PROG
(PARI) nbe(n) = {my(f = factor(n!)[, 2], nb = 0); for (i=1, #f, if (!(f[i] % 2), nb++, break); ); nb; }
a(n) = {my(i = 1); while (nbe(i) != n, i++); i; } \\ Michel Marcus, Nov 07 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev and Peter J. C. Moses, Apr 07 2014
EXTENSIONS
a(21)-a(30) from Giovanni Resta, Apr 07 2014
a(31)-a(33) from Hiroaki Yamanouchi, Sep 05 2014
STATUS
approved