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 A123113 Main diagonal of prime power sum array. 5

%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

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Last modified December 15 11:43 EST 2019. Contains 329999 sequences. (Running on oeis4.)