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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. 1
1, 3, 35, 899, 44099, 5336099, 901800899, 260620460099, 94083986096099, 49770428644836899, 41856930490307832899, 40224510201185827416899, 55067354465423397733736099, 92568222856376731590410384099 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sequence generalized: a(0)=1; a(n) = (Product_{i=1..n} p(i)^r) - 1, where p(i) is the i-th prime.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..100

A. Adelberg, S. Hong and W. Ren, Bounds on divided universal Bernoulli numbers and universal Kummer congruences, Proc. Amer. Math. Soc., Volume 136, Number 1, 2008, Pages 61-71,

Alexei A. Panchishkin, Generalized Kummer congruences and p-adic families of motives, arXiv:math/9503218 [math.NT], 1995.

FORMULA

a(n) = A061742(n-1)-1 = (A002110(n)+1)*(A002110(n)-1) for n>1. - R. J. Mathar, Feb 28 2008

MAPLE

A002110 := proc(n) mul(ithprime(i), i=1..n) ; end:

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

MATHEMATICA

Join[{1}, Rest[#-1&/@FoldList[Times, 1, Prime[Range[15]]^2]]] (* Harvey P. Dale, Oct 02 2011 *)

Join[{1}, Table[Product[Prime[i]^(2), {i, 1, n}] - 1, {n, 1, 15}]] (* G. C. Greubel, Oct 17 2016 *)

PROG

(PARI) a(n) = prod(k=1, n, prime(k)^2) - 1; \\ Michel Marcus, Oct 17 2016

CROSSREFS

Cf. A057588, A057705, A002110.

Sequence in context: A185752 A210897 A267221 * A231644 A287405 A107712

Adjacent sequences:  A135513 A135514 A135515 * A135517 A135518 A135519

KEYWORD

easy,nonn

AUTHOR

Ctibor O. Zizka, Feb 19 2008

STATUS

approved

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Last modified June 4 02:54 EDT 2020. Contains 334812 sequences. (Running on oeis4.)