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A256625 Product of the first n lucky numbers.

%I A256625 #30 Jul 17 2015 02:03:21
%S A256625 1,3,21,189,2457,36855,773955,19348875,599815125,19793899125,
%T A256625 732374267625,31492093507875,1543112581885875,78698741676179625,
%U A256625 4958020725599316375,332187388615154197125,22920929814445639601625,1673227876454531690918625,125492090734089876818896875,9913875167993100268692853125
%N A256625 Product of the first n lucky numbers.
%C A256625 For all n A057616(n)=a(m) for some m, that is, A256625 is a superset of A057616.
%H A256625 Robert Israel, <a href="/A256625/b256625.txt">Table of n, a(n) for n = 1..315</a>
%F A256625 a(n+1) = a(n)*A000959(n+1).
%F A256625 a(n) > A002110(n) > A000142(n) for all n>1 (conjectured).
%F A256625 A000312(n) = o(a(n)) where o(a(n)) is "little o" notation (conjectured).
%F A256625 Sum_{k >=1} 1/a(n) = 1.386678865477327..., the sum converges because the inequality a(n) > A000142(n) holds for large enough n.
%e A256625 For n=4, a(4) = A000959(1)*A000959(2)*A000959(3)*A000959(4) = 1*3*7*9 = 189.
%p A256625 N:= 100:  # to use all lucky numbers <= N
%p A256625 L:= [seq(2*i+1, i=0..N)]:
%p A256625 for n from 2 while n < nops(L) do
%p A256625   r:= L[n];
%p A256625   L:= subsop(seq(r*i=NULL, i=1..nops(L)/r), L);
%p A256625 od:
%p A256625 seq(convert(L[1..n],`*`),n=1..nops(L)) ;  # _Robert Israel_, Jul 14 2015
%t A256625 luckies = 2*Range@ 200 - 1; f[n_] := Block[{k = luckies[[n]]}, luckies = Delete[luckies, Table[{k}, {k, k, Length@ luckies, k}]]]; Do[f@ n, {n, 2, 30}]; Table[Times @@ Take[luckies, n], {n, 20}] (* _Michael De Vlieger_, Jul 12 2015, based on code from _Robert G. Wilson v_ at A000959 *)
%Y A256625 Cf. A000959 (lucky numbers).
%Y A256625 Cf. A000142 (factorial), A002110 (product of the first n primes).
%Y A256625 Cf. A057616 (subset).
%K A256625 easy,nonn
%O A256625 1,2
%A A256625 _Chayim Lowen_, Jul 11 2015
%E A256625 a(12)-a(20) from _Michael De Vlieger_, Jul 12 2015