A061720 First differences of sequence of primorials.

1, 4, 24, 180, 2100, 27720, 480480, 9189180, 213393180, 6246600360, 194090796900, 7220177644680, 296829525392400, 12778511068142820, 601807021256821380, 31974268694601553320, 1890171191677022594340, 115365621009252758344200, 7741033169720860084895820

Offset: 0

Author

Labos Elemer, Jun 20 2001

Keywords

• easy
• nonn

Comments

Largest number below primorial(n + 1) to be divisible by the first n primes. - Alonso del Arte, Dec 13 2014

Examples

			a(2) = primorial(3) - primorial(2) = 30 - 6 = 24.
a(3) = primorial(4) - primorial(3) = 210 - 30 = 180.
		

Links

• Harry J. Smith, Table of n, a(n) for n=0..100
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A006093, A286629.

Subsequence of A276155.

Programs

Maple

p:= proc(n) option remember; `if`(n=0, 1, ithprime(n)*p(n-1)) end:
a:= n-> p(n+1)-p(n):
seq(a(n), n=0..20);  # Alois P. Heinz, Feb 23 2022

Mathematica

Differences[FoldList[Times, 1, Prime[Range[20]]]] (* Alonso del Arte, Dec 13 2014 *)

PARI

{ n=-1; r=q=1; forprime (p=2, prime(101), r*=p; write("b061720.txt", n++, " ", r-q); q=r ) } \\ Harry J. Smith, Jul 27 2009

Formula

a(n) = A002110(n+1) - A002110(n) = A002110(n)*A006093(n+1).

Extensions

Since primorial(0) = 1, term a(0) = 1 added by Harry J. Smith, Jul 27 2009