1,1

a(n) is prime for n = 3, 4, ..., a(n) is semiprime for n = 7, 8, 11, ...

a(n) = sum[i = 1 to n]A001358(i)^A000040(i).

a(1) = 16 because semiprime(1)^prime(1) = 4^2 = 16.

a(2) = 232 because 4^2 + 6^3 = 232.

a(3) = 59281 = 4^2 + 6^3 + 9^5, which is a prime.

a(4) = 10059281 = 4^2 + 6^3 + 9^5 + 10^7, which is a prime.

a(7) = 4^2 + 6^3 + 9^5 + 10^7 + 14^11 + 15^13 + 21^17 = 428081461 * 70178102025601, which is semiprime.

a(8) = 4^2 + 6^3 + 9^5 + 10^7 + 14^11 + 15^13 + 21^17 + 22^19 = 47 * 682872748031142382580827, which is semiprime.

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.

Cf. A000040, A001358, A137701, A125580.

Sequence in context: A048445 A028340 A119463 this_sequence A161591 A103975 A060198

Adjacent sequences: A111093 A111094 A111095 this_sequence A111097 A111098 A111099

easy,nonn,less

Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 13 2005