

A241124


Smallest k such that the factorization of k! over distinct terms of A050376 contains at least n nonprime terms of A050376.


4



4, 6, 8, 12, 14, 15, 16, 24, 25, 26, 30, 32, 46, 46, 48, 48, 62, 63, 63, 64, 64, 87, 91, 95, 96, 96, 96, 114, 114, 122, 124, 125, 128, 129, 160, 161, 176, 177, 178, 178, 188, 189, 190, 192, 192, 192, 194, 225, 226, 226, 240, 252, 254, 255, 256, 288, 288, 289, 290, 320
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OFFSET

1,1


LINKS



EXAMPLE

For k=2,3,4,5,6, we have the following factorizations of k! over distinct terms of A050376: 2!=2, 3!=2*3, 4!=2*3*4, 5!=2*3*4*5, 6!=5*9*16.
Therefore, a(1)=4, a(2)=6.


MATHEMATICA

f[n_] := DigitCount[n, 2, 1]  Mod[n, 2]; nb[n_] := Total@(f/@ FactorInteger[n][[;; , 2]]); a[n_] := (k=1; While[nb[k!] < n, k++]; k); Array[a, 60] (* Amiram Eldar, Dec 16 2018 from the PARI code *)


PROG

(PARI) nb(n) = {my(f = factor(n)); sum(k=1, #f~, hammingweight(f[k, 2])  (f[k, 2] % 2)); }
a(n) = {my(k=1); while (nb(k!) < n, k++); k; } \\ Michel Marcus, Dec 16 2018


CROSSREFS

Cf. A240537, A240606, A240619, A240620, A240668, A240669, A240670, A240672, A240695, A240751, A240755, A240764, A240905, A240906, A241123.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



