%I A138564
%S A138564 1,9,225,14049,1742049,374990049,128399054049,65676719822049,
%T A138564 47850402559694049,47832576242431694049,63649302669112063694049,
%U A138564 109966989623147836159694049,241567605673714904675071694049
%N A138564 a(1) = 1; a(n) = a(n-1) + (n!)^3.
%C A138564 By sum of cubes factorization, every a(n) > 1 is a multiple of 9, hence 
               none of these are prime, unlike the case of sum of squares of factorials 
               (i.e. (1!)^2 + (2!)^2+ (3!)^2+ (4!)^2 = 617 is prime; 41117342095090841723228045851817 
               = (1!)^2 + (2!)^2 + (3!)^2 + (4!)^2 + (5!)^2 + (6!)^2 + (7!)^2 + 
               (8!)^2 + (9!)^2 + (10!)^2 + (11!)^2 + (12!)^2 + (13!)^2 + (14!)^2 
               + (15!)^2 + (16!)^2 + (17!)^2 + (18!)^2 is prime).
%F A138564 a(n) = SUM{k=1..n] (k!)^3 = SUM[k=1..n] A000578(A000142(n)).
%e A138564 a(18) = (1!)^3 + (2!)^3 + (3!)^3 + (4!)^3 + (5!)^3 + (6!)^3 + (7!)^3 
               + (8!)^3 + (9!)^3 + (10!)^3 + (11!)^3 + (12!)^3 + (13!)^3 + (14!)^3 
               + (15!)^3 + (16!)^3 + (17!)^3 + (18!)^3 = 262480797594664584673157017306412926841599694049.
%Y A138564 Cf. A000142, A000578, A104344, A100288.
%Y A138564 Sequence in context: A128492 A001818 A095363 this_sequence A158728 A152101 
               A165389
%Y A138564 Adjacent sequences: A138561 A138562 A138563 this_sequence A138565 A138566 
               A138567
%K A138564 easy,nonn
%O A138564 1,2
%A A138564 Jonathan Vos Post (jvospost3(AT)gmail.com), May 18 2008