A111096 Partial sums of A137701.

16, 232, 59281, 10059281, 4049575228945, 1950244643588320, 30041944445326335483061, 32095019157463691981298869, 142108579247039194637916834814494, 108199957883829576141601541930838816381470, 118558455387984539329682688832638841343258239487

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..11.

Formula

a(n) = Sum_{i=1..n} A001358(i)^A000040(i).

Example

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.

Crossrefs

Cf. A000040, A001358, A137701, A125580.

Sequence in context: A222389 A222938 A265469 * A283853 A266099 A264343

Adjacent sequences: A111093 A111094 A111095 * A111097 A111098 A111099

Keyword

easy,nonn,less

Author

Jonathan Vos Post, Oct 13 2005

Status

approved