login
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
OFFSET
0,2
COMMENTS
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.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..99 [Offset shifted by Georg Fischer, Jun 18 2021]
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) = if(n==0, 1, prod(k=1, n, prime(k)^2) - 1); \\ Michel Marcus, Oct 17 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ctibor O. Zizka, Feb 19 2008
EXTENSIONS
Offset corrected by Georg Fischer, Jun 18 2021
STATUS
approved