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%I #7 Sep 26 2024 23:35:05
%S 1,129,280065,4586751489,358322666751489,100306488365546751489,
%T 82606511560391889386751489,173238283180457843219993066751489,
%U 828593116199250458889895450218986751489
%N a(1) = 1; a(n) = a(n-1) + (n!)^7.
%C After a(1) = 1 these are all divisible by 3. a(n)/3 is prime (i.e. a(n) is semiprime) for n = 2, 4 (i.e. (1!)^7 + (2!)^7 + (3!)^7 + (4!)^7 = 4586751489 = 3 * 1528917163) and then when next?
%F a(n) = Sum_{k=1..n} (k!)^7 = Sum_{k=1..n} A001015(A000142(n)).
%Y Cf. A000142, A001015, A104344, A100288.
%K easy,nonn
%O 1,2
%A _Jonathan Vos Post_, May 18 2008