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%I #17 Sep 08 2022 08:45:28
%S 2,13,280,17489,48909526,13423779037,232729381165100,
%T 146367546237420097,8864305651125125485354,
%U 100000100010100010100010101101,193529735150413879906083607547512
%N Main diagonal of prime power sum array.
%C Main diagonal of the infinite array T(k,n) = 1 + Sum_{i=1..k} n^prime(i).
%C a(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
%H G. C. Greubel, <a href="/A123113/b123113.txt">Table of n, a(n) for n = 1..75</a>
%F a(n) = 1 + n^2 + n^3 + n^5 + ... + n^prime(n).
%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 *)
%o (Magma) [1 + (&+[n^NthPrime(j): j in [1..n]]): n in [1..15]]; // _G. C. Greubel_, Jul 21 2021
%o (Sage) [1 + sum(n^nth_prime(j) for j in (1..n)) for n in (1..15)] # _G. C. Greubel_, Jul 21 2021
%Y Cf. A000040, A062481.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Sep 28 2006
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