A087316 a(n) = Sum_{k=1..n} prime(k)^prime(n-k+1).

4, 17, 84, 545, 7824, 281771, 51540600, 3347558057, 1146374959980, 288113965730819, 529172633067826888, 283453407513524913023, 4122282265785671687518812, 1586581830624893452605127040309, 412109111737176949907195758658736

Offset: 1

Author

Amarnath Murthy, Sep 03 2003

Keywords

• nonn

Examples

			Examples from _Jonathan Vos Post_, Jan 06 2006: (Start)
a(1) = 4 because prime(1)^prime(1) = 2^2 = 4.
a(2) = 17 because prime(1)^prime(2) + prime(2)^prime(1) = 2^3 + 3^2 = 17.
a(3) = 84 because 2^5 + 3^3 + 5^2 = 84.
a(4) = 545 = 2^7 + 3^5 + 5^3 + 7^2.
a(5) = 7824 = 2^11 + 3^7 + 5^5 + 7^3 + 11^2.
a(6) = 281771 = 2^13 + 3^11 + 5^7 + 7^5 + 11^3 + 13^2.
a(7) = 51540600 = 2^17 + 3^13 + 5^11 + 7^7 + 11^5 + 13^3 + 17^2.
a(8) = 3347558057 = 2^19 + 3^17 + 5^13 + 7^11 + 11^7 + 13^5 + 17^3 + 19^2.
a(9) = 1146374959980 = 2^23 + 3^19 + 5^17 + 7^13 + 11^11 + 13^7 + 17^5 + 19^3 + 23^2. (End)
		

Links

• T. D. Noe, Table of n, a(n) for n=1..50

Crossrefs

Cf. A000040, A005408, A087315, A113122, A113153, A113154.

Programs

Maple

a:=n->sum(ithprime(k)^ithprime(n-k+1),k=1..n): seq(a(n),n=1..16); # Emeric Deutsch, Apr 13 2005

Mathematica

Table[Sum[Prime[k]^Prime[n - k + 1], {k, 1, n}], {n, 1, 15}] (* Vaclav Kotesovec, Jun 08 2025 *)

PARI

a(n) = sum(k=1, n, prime(k)^prime(n-k+1)); \\ Michel Marcus, Aug 20 2019

Python

from sympy import prime
def a(n): return sum(prime(k)**prime(n-k+1) for k in range(1, n+1))
print([a(n) for n in range(1, 16)]) # Michael S. Branicky, Apr 17 2021

Extensions

More terms from Sam Alexander, Oct 20 2003

Further terms from Emeric Deutsch, Apr 13 2005

Edited by N. J. A. Sloane, Aug 19 2008 at the suggestion of R. J. Mathar