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A123113 Main diagonal of prime power sum array. 5
2, 13, 280, 17489, 48909526, 13423779037, 232729381165100, 146367546237420097, 8864305651125125485354, 100000100010100010100010101101, 193529735150413879906083607547512 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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?

The next prime in the sequence is for n = 20. It has 93 digits. - Harvey P. Dale, Jan 18 2017

LINKS

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

FORMULA

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).

EXAMPLE

a(1) = 2 = 1+1^2.

a(2) = 13 = 1+2^2+2^3.

a(3) = 280 = 1+3^2+3^3+3^5.

a(4) = 17489 = 1+4^2+4^3+4^5+4^7.

a(5) = 48909526 = 1+5^2+5^3+5^5+5^7+5^11.

a(6) = 13423779037 = 1+6^2+6^3+6^5+6^7+6^11+6^13.

a(7) = 232729381165100 = 1+7^2+7^3+7^5+7^7+7^11+7^13+7^17.

a(8) = 146367546237420097 = 1+8^2+8^3+8^5+8^7+8^11+8^13+8^17+8^19.

MATHEMATICA

Table[Total[n^Prime[Range[n]]]+1, {n, 15}] (* Harvey P. Dale, Jan 18 2017 *)

CROSSREFS

Cf. A000040, A062481.

Sequence in context: A134296 A086510 A326360 * A126742 A013051 A012955

Adjacent sequences:  A123110 A123111 A123112 * A123114 A123115 A123116

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Sep 28 2006

STATUS

approved

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Last modified November 19 20:42 EST 2019. Contains 329323 sequences. (Running on oeis4.)