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%I #6 Jul 29 2022 09:01:28
%S 16,232,59281,10059281,4049575228945,1950244643588320,
%T 30041944445326335483061,32095019157463691981298869,
%U 142108579247039194637916834814494,108199957883829576141601541930838816381470,118558455387984539329682688832638841343258239487
%N Partial sums of A137701.
%C a(n) is prime for n = 3, 4, ..., a(n) is semiprime for n = 7, 8, 11, ...
%F a(n) = Sum_{i=1..n} A001358(i)^A000040(i).
%e a(1) = 16 because semiprime(1)^prime(1) = 4^2 = 16.
%e a(2) = 232 because 4^2 + 6^3 = 232.
%e a(3) = 59281 = 4^2 + 6^3 + 9^5, which is a prime.
%e a(4) = 10059281 = 4^2 + 6^3 + 9^5 + 10^7, which is a prime.
%e a(7) = 4^2 + 6^3 + 9^5 + 10^7 + 14^11 + 15^13 + 21^17 = 428081461 * 70178102025601, which is semiprime.
%e a(8) = 4^2 + 6^3 + 9^5 + 10^7 + 14^11 + 15^13 + 21^17 + 22^19 = 47 * 682872748031142382580827, which is semiprime.
%e a(11) = 4^2 + 6^3 + 9^5 + 10^7 + 14^11 + 15^13 + 21^17 + 22^19 + 25^23 + 26^29 + 33^31 = 17 * 6974026787528502313510746401919931843721072911 which is semiprime.
%Y Cf. A000040, A001358, A137701, A125580.
%K easy,nonn,less
%O 1,1
%A _Jonathan Vos Post_, Oct 13 2005
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