

A240695


a(n) is the smallest k such that a unique product of distinct terms of A050376 which is equal to k! contains at least the first n terms of A050376.


12



2, 3, 4, 5, 125, 125, 138, 220, 220, 1766, 5526, 10351, 12365, 65653, 65653, 202738, 490333, 808762, 1478432, 1971352, 1971352, 1971352, 14798206, 14798206, 14798206, 14798206, 161974053, 547880880, 1619543840, 1619543840, 1619543840, 2103844465, 6435961044
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OFFSET

1,1


COMMENTS

By the definition, the representation of a(n)! as a product of distinct terms of A050376 should contain the first n terms of A050376 and there is no restriction on the distribution of other factors of this product.
a(38) > 2 * 10^11.  Hiroaki Yamanouchi, Oct 01 2014


LINKS

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..37


EXAMPLE

5! = 2*3*4*5. We have the first 4 terms of A050376, so a(4) = 5.


MATHEMATICA

bad[n_, pp_, mo_] := Catch[Do[If[ Mod[(n  Total@ IntegerDigits[n, pp[[i]]]) /(pp[[i]]  1), mo[[i]] + 1] != mo[[i]], Throw@ True], {i, Length@ pp}]; False]; a[n_]:= Block[{fa, mo, pp, k}, fa = FactorInteger[ Times @@ Select[Range[2, Prime[n]], (f = FactorInteger@# ; Length[f] == 1 && IntegerQ[Log[2, f[[1, 2]]]]) &, n]]; pp = First /@ fa; mo = Last /@ fa; k = fa[[1, 1]]; While[ bad[k, pp, mo], k++]; k]; Array[a, 15] (* Giovanni Resta, Apr 11 2014 *)


CROSSREFS

Cf. A240537, A240606, A240619, A240620, A240668, A240669, A240670, A240672.
Sequence in context: A010348 A171591 A140432 * A004867 A318842 A298671
Adjacent sequences: A240692 A240693 A240694 * A240696 A240697 A240698


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Apr 10 2014


EXTENSIONS

a(5)a(23) from Giovanni Resta, Apr 11 2014
a(24)a(33) from Hiroaki Yamanouchi, Oct 01 2014


STATUS

approved



