A141535 An eighth of the product of three integers surrounding the (n+1)-st prime, minus half of the product of the 3 numbers surrounding n+1.

0, 3, 12, 105, 168, 444, 603, 1158, 2550, 3060, 5469, 7518, 8568, 11292, 16563, 23217, 25458, 34167, 40740, 43998, 56307, 65391, 81210, 106272, 120000, 126750, 142155, 149685, 166863, 241152

Offset: 1

Author

Roger L. Bagula, Aug 12 2008

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Maple

A127917 := proc(n) p := ithprime(n) ; (p-1)*p*(p+1) ; end: A027480 := proc(n) n*(n+1)*(n+2)/2 ; end: A := proc(n) A127917(n+1)/8-A027480(n) ; end: for n from 1 to 40 do printf("%d,",A(n)) ; od: # R. J. Mathar, Aug 20 2008

Mathematica

a[n_] = (Prime[n + 1] - 1)*Prime[n + 1]*(Prime[n + 1] + 1)/8 - n*(n + 1)*(n + 2)/2; Table[a[n], {n, 1, 30}]
f[n_]:=Module[{pr=Prime[n+1],n1=n+1},(pr(pr^2-1))/8-(n1(n1^2-1))/2]; Array[f,30] (* Harvey P. Dale, May 24 2012 *)

Formula

a(n) = A127917(n+1)/8-A027480(n) = {p(n+1)-1}*p(n+1)*{p(n+1)+1}/8-n(n+1)(n+2)/2.

Extensions

Edited by N. J. A. Sloane, Aug 23 2008