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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.

%I A141535 #7 May 24 2012 05:14:56
%S A141535 0,3,12,105,168,444,603,1158,2550,3060,5469,7518,8568,11292,16563,
%T A141535 23217,25458,34167,40740,43998,56307,65391,81210,106272,120000,126750,
%U A141535 142155,149685,166863,241152
%N 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.
%H A141535 Harvey P. Dale, <a href="/A141535/b141535.txt">Table of n, a(n) for n = 1..1000</a>
%F A141535 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.
%p A141535 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
%t A141535 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}]
%t A141535 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 *)
%K A141535 nonn
%O A141535 1,2
%A A141535 _Roger L. Bagula_, Aug 12 2008
%E A141535 Edited by _N. J. A. Sloane_, Aug 23 2008