%I
%S 2,13,280,17489,48909526,13423779037,232729381165100,
%T 146367546237420097,8864305651125125485354,
%U 100000100010100010100010101101,193529735150413879906083607547512
%N Main diagonal of prime power sum array.
%C Also see A062481(n) = n^prime(n). A(n,n) is prime for n = 1, 2, 4  what is the next prime in the sequence?
%C The next prime in the sequence is for n = 20. It has 93 digits.  _Harvey P. Dale_, Jan 18 2017
%F a(n) = 1 + n^2 + n^3 + n^5 + ... + n^prime(n). = Main diagonal A(n,n), of the infinite array A(k,n) = 1 + SUM[i=1..k]n^prime(i). If we deem prime(0) = 1, the array is A(k,n) = SUM[i=0..k]n^prime(i).
%e a(1) = 2 = 1+1^2.
%e a(2) = 13 = 1+2^2+2^3.
%e a(3) = 280 = 1+3^2+3^3+3^5.
%e a(4) = 17489 = 1+4^2+4^3+4^5+4^7.
%e a(5) = 48909526 = 1+5^2+5^3+5^5+5^7+5^11.
%e a(6) = 13423779037 = 1+6^2+6^3+6^5+6^7+6^11+6^13.
%e a(7) = 232729381165100 = 1+7^2+7^3+7^5+7^7+7^11+7^13+7^17.
%e a(8) = 146367546237420097 = 1+8^2+8^3+8^5+8^7+8^11+8^13+8^17+8^19.
%t Table[Total[n^Prime[Range[n]]]+1,{n,15}] (* _Harvey P. Dale_, Jan 18 2017 *)
%Y Cf. A000040, A062481.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Sep 28 2006
