A054640 a(n) is the sum of the divisors of the n-th primorial: a(n) = A000203(A002110(n)).

1, 3, 12, 72, 576, 6912, 96768, 1741824, 34836480, 836075520, 25082265600, 802632499200, 30500034969600, 1281001468723200, 56364064623820800, 2705475101943398400, 146095655504943513600, 8765739330296610816000, 543475838478389870592000, 36956357016530511200256000

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, 1, n}], {n, 1, 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 [2..19]]; // Vincenzo Librandi, May 08 2017

Crossrefs

Cf. A002110, A000203, A005867, A028815, A054641, A073004.

Sequence in context: A337061 A147998 A052676 * A139486 A260622 A348222

Adjacent sequences: A054637 A054638 A054639 * A054641 A054642 A054643

Keyword

nonn

Author

Labos Elemer, May 15 2000

Extensions

a(0)=1 prepended by Alois P. Heinz, Apr 01 2021

Status

approved