A066264 Number of composites < primorial(p) with all prime factors > p.

0, 0, 0, 5, 141, 2517, 49835, 1012858, 24211837, 721500293, 22627459400, 844130935667, 34729870646917, 1491483322755273, 69890000837179156

Offset: 1

Author

Patrick De Geest, Dec 10 2001

Keywords

• nonn

Comments

There is a simple relationship between this sequence and the number of primes < primorial(p), as given by A000849 and sequence A005867 which gives the number of composites in primorial(p+1) having (p+1) as their lowest prime factor: a(n) = n + A005867(n) - A000849(n) - 1. - Dennis Martin (dennis.martin(AT)dptechnology.com), Apr 15 2007

Examples

			There are 5 composites < primorial(7) or 210 and whose prime factors are all larger than 7: 121 (11*11), 143 (11*13), 169 (13*13), 187 (11*17) and 209 (11*19).
		

Links

• Eric Weisstein's World of Mathematics, Primorial

Crossrefs

Cf. A000849, A002110, A005867.

Programs

Mathematica

Array[#1 + EulerPhi@ #2 - PrimePi@ #2 - 1 & @@ {#, Product[Prime@ i, {i, #}]} &, 12] (* Michael De Vlieger, Apr 03 2019 *)

Formula

a(n) = n + A005867(n) - A000849(n) - 1. - Michael De Vlieger, Apr 03 2019, citing Dennis Martin's comment above.

Extensions

More terms from Dennis Martin (dennis.martin(AT)dptechnology.com), Apr 15 2007

Offset corrected by Charles J. Daniels (chajadan(AT)gmail.com), Dec 06 2009

a(14)-a(15) from Donovan Johnson, May 03 2010