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A135516 a(0)=1; a(n) = (Product_{i=1..n} prime(i)^2) - 1, where prime(i) is the i-th prime.

%I A135516 #25 Jun 18 2021 02:39:17
%S A135516 1,3,35,899,44099,5336099,901800899,260620460099,94083986096099,
%T A135516 49770428644836899,41856930490307832899,40224510201185827416899,
%U A135516 55067354465423397733736099,92568222856376731590410384099
%N A135516 a(0)=1; a(n) = (Product_{i=1..n} prime(i)^2) - 1, where prime(i) is the i-th prime.
%C A135516 Sequence can be generalized: a(0)=1; a(n) = (Product_{i=1..n} prime(i)^r) - 1, where prime(i) is the i-th prime.
%H A135516 G. C. Greubel, <a href="/A135516/b135516.txt">Table of n, a(n) for n = 0..99</a> [Offset shifted by _Georg Fischer_, Jun 18 2021]
%H A135516 A. Adelberg, S. Hong and W. Ren, <a href="https://doi.org/10.1090/S0002-9939-07-09025-9">Bounds on divided universal Bernoulli numbers and universal Kummer congruences</a>, Proc. Amer. Math. Soc., Volume 136, Number 1, 2008, Pages 61-71,
%H A135516 Alexei A. Panchishkin, <a href="https://arxiv.org/abs/math/9503218">Generalized Kummer congruences and p-adic families of motives</a>, arXiv:math/9503218 [math.NT], 1995.
%F A135516 a(n) = A061742(n-1)-1 = (A002110(n)+1)*(A002110(n)-1) for n>1. - _R. J. Mathar_, Feb 28 2008
%p A135516 A002110 := proc(n) mul(ithprime(i),i=1..n) ; end:
%p A135516 A135516 := proc(n) if n =0 then 1; else (A002110(n)+1)*(A002110(n)-1) ; fi ; end: seq(A135516(n),n=0..20) ; # _R. J. Mathar_, Feb 28 2008
%t A135516 Join[{1},Rest[#-1&/@FoldList[Times,1,Prime[Range[15]]^2]]] (* _Harvey P. Dale_, Oct 02 2011 *)
%t A135516 Join[{1}, Table[Product[Prime[i]^(2), {i,1,n}] - 1, {n,1,15}]] (* _G. C. Greubel_, Oct 17 2016 *)
%o A135516 (PARI) a(n) = if(n==0, 1, prod(k=1, n, prime(k)^2) - 1); \\ _Michel Marcus_, Oct 17 2016
%Y A135516 Cf. A057588, A057705, A002110.
%K A135516 easy,nonn
%O A135516 0,2
%A A135516 _Ctibor O. Zizka_, Feb 19 2008
%E A135516 Offset corrected by _Georg Fischer_, Jun 18 2021