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 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 (list; graph; refs; listen; history; text; internal format)
 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. Sequence in context: A179852 A281020 A110606 * A117247 A249722 A047407 Adjacent sequences:  A241121 A241122 A241123 * A241125 A241126 A241127 KEYWORD nonn AUTHOR Vladimir Shevelev, Apr 16 2014 EXTENSIONS More terms from Michel Marcus, Dec 16 2018 STATUS approved

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Last modified April 22 14:33 EDT 2021. Contains 343177 sequences. (Running on oeis4.)