A256625 Product of the first n lucky numbers.

1, 3, 21, 189, 2457, 36855, 773955, 19348875, 599815125, 19793899125, 732374267625, 31492093507875, 1543112581885875, 78698741676179625, 4958020725599316375, 332187388615154197125, 22920929814445639601625, 1673227876454531690918625, 125492090734089876818896875, 9913875167993100268692853125

Offset: 1

Author

Chayim Lowen, Jul 11 2015

Keywords

• easy
• nonn

Comments

For all n A057616(n)=a(m) for some m, that is, A256625 is a superset of A057616.

Examples

			For n=4, a(4) = A000959(1)*A000959(2)*A000959(3)*A000959(4) = 1*3*7*9 = 189.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..315

Crossrefs

Cf. A000959 (lucky numbers).

Cf. A000142 (factorial), A002110 (product of the first n primes).

Cf. A057616 (subset).

Programs

Maple

N:= 100:  # to use all lucky numbers <= N
L:= [seq(2*i+1, i=0..N)]:
for n from 2 while n < nops(L) do
  r:= L[n];
  L:= subsop(seq(r*i=NULL, i=1..nops(L)/r), L);
od:
seq(convert(L[1..n],`*`),n=1..nops(L)) ;  # Robert Israel, Jul 14 2015

Mathematica

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 *)

Formula

a(n+1) = a(n)*A000959(n+1).

a(n) > A002110(n) > A000142(n) for all n>1 (conjectured).

A000312(n) = o(a(n)) where o(a(n)) is "little o" notation (conjectured).

Sum_{k >=1} 1/a(n) = 1.386678865477327..., the sum converges because the inequality a(n) > A000142(n) holds for large enough n.

Extensions

a(12)-a(20) from Michael De Vlieger, Jul 12 2015