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%I #38 Apr 08 2020 07:25:59
%S 12,6,10,20,48,54,338,875,2849,1440,3841,816,59583,101755,40465,37514,
%T 409026,268836,591360,855368,5493420,9627251,28953290,14557116,
%U 7336812,1475128,127632241,531296823,3028478192,2435868325,1092228841,32377733790,472077979
%N Let a(n) be the least k such that in the prime power factorization of k! the exponents of primes p_1, ...,p_n are even, while the exponent of p_(n+1) is odd.
%C 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).
%D P. Erdős, P. L. Graham, Old and new problems and results in combinatorial number theory, L'Enseignement Mathematique, Imprimerie Kunding, Geneva, 1980.
%H Giovanni Resta, <a href="/A240537/b240537.txt">Table of n, a(n) for n = 1..46</a> (first 36 terms from Hiroaki Yamanouchi)
%H D. Berend, <a href="http://dx.doi.org/10.1006/jnth.1997.2106">Parity of exponents in the factorization of n!</a>, J. Number Theory, 64 (1997), 13-19.
%H Y.-G. Chen, <a href="http://dx.doi.org/10.1016/S0022-314X(03)00013-1">On the parity of exponents in the standard factorization of n!</a>, J. Number Theory, 100 (2003), 326-331.
%o (PARI) nbe(n) = {my(f = factor(n!)[, 2], nb = 0); for (i=1, #f, if (!(f[i] % 2), nb++, break);); nb;}
%o a(n) = {my(i = 1); while (nbe(i) != n, i++); i;} \\ _Michel Marcus_, Nov 07 2018
%Y Cf. A115627, A240620.
%K nonn
%O 1,1
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Apr 07 2014
%E a(21)-a(30) from _Giovanni Resta_, Apr 07 2014
%E a(31)-a(33) from _Hiroaki Yamanouchi_, Sep 05 2014
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