OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Rafael Jakimczuk, Two Topics in Number Theory: Sum of Divisors of the Primorial and Sum of Squarefree Parts, International Mathematical Forum, Vol. 12, No. 7 (2017), pp. 331-338.
FORMULA
a(n+1) = a(n)*(prime(n) + 1) = a(n)*A028815(n) (quotient=n-th prime+1 starting with 2).
a(n) ~ (6/Pi^2) * exp(gamma) * A002110(n) * log(prime(n)) + O(A002110(n)) (Jakimczuk, 2017). - Amiram Eldar, Feb 17 2021
a(n) = a(n-1) * A008864(n). - Flávio V. Fernandes, Mar 20 2021
MAPLE
a:= n-> mul(1+ithprime(j), j=1..n): seq(a(n), n=0..20); # Zerinvary Lajos, Aug 24 2008
MATHEMATICA
Table[Product[1 + Prime[i], {i, n-1}], {n, 100}] (* Geoffrey Critzer, Dec 01 2014 *)
PROG
(PARI) a(n)=prod(i=1, n, prime(i)+1) \\ Charles R Greathouse IV, Feb 13 2013
(Magma) [1/2*&*[(1+NthPrime(k)): k in [0..n-1]]: n in [1..19]]; // Vincenzo Librandi, May 08 2017
(SageMath)
def A054640(n): return product(nth_prime(j)+1 for j in range(1, n+1))
[A054640(n) for n in range(41)] # G. C. Greubel, Aug 05 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, May 15 2000
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Apr 01 2021
STATUS
approved