A241124 Smallest k such that the factorization of k! over distinct terms of A050376 contains at least n nonprime terms of A050376.

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

Offset

1,1

Links

Table of n, a(n) for n=1..60.

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: A281020 A110606 A346124 * 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