

A241123


Smallest k such that the factorization of k! over distinct terms of A050376 contains exactly n primes.


6



2, 3, 5, 13, 17, 21, 23, 37, 33, 42, 43, 56, 59, 57, 75, 84, 99, 101, 105, 109, 123, 119, 133, 139, 157, 162, 163, 182, 186, 183, 207, 208, 222, 219, 235, 220, 255, 257, 263, 268, 267, 303, 305, 307, 316, 315, 340, 344, 341, 343, 383, 385, 387, 397, 411, 425
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OFFSET

1,1


REFERENCES

V. S. Shevelev, Multiplicative functions in the FermiDirac arithmetic, Izvestia Vuzov of the NorthCaucasus region, Nature sciences 4 (1996), 2843 (Russian; MR 2000f: 11097, pp. 39123913).


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..500
S. Litsyn and V. S. Shevelev, On factorization of integers with restrictions on the exponent, INTEGERS: Electronic Journal of Combinatorial Number Theory, 7 (2007), #A33, 136.


EXAMPLE

Factorization of 5! over distinct terms of A050376 is 5! = 2*3*4*5. Thus 5 is the smallest k such that such a factorization contains 3 primes: 2,3,5. So a(3)=5.


MATHEMATICA

f[p_, e_] := Mod[e, 2]; b[1] = 0; b[n_] := Plus @@ (f @@@ FactorInteger[n]); m = 56; v = Table[0, {m}]; c = 0; p = 1; n = 2; While[c < m, p *= n; i = b[p]; If[i <= m && v[[i]] == 0, c++; v[[i]] = n]; n++]; v (* Amiram Eldar, Sep 17 2019 *)


PROG

(PARI) nbp(n) = {f = factor(n); sum (i=1, #f~, f[i, 2] % 2); }
a(n) = {k = 1; while(nbp(k!) != n, k++); k; } \\ Michel Marcus, Apr 27 2014


CROSSREFS

Cf. A240537, A240606, A240619, A240620, A240668, A240669, A240670, A240672, A240695, A240751, A240755, A240764, A240905, A240906.
Sequence in context: A236183 A093077 A249016 * A038983 A235635 A253645
Adjacent sequences: A241120 A241121 A241122 * A241124 A241125 A241126


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Apr 16 2014


EXTENSIONS

More terms from Peter J. C. Moses, Apr 17 2014


STATUS

approved



