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

1,4

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

Links

Table of n, a(n) for n=1..15.

Eric Weisstein's World of Mathematics, Primorial

Formula

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

Example

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).

Mathematica

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

Crossrefs

Cf. A000849, A002110, A005867.

Sequence in context: A136464 A203523 A006269 * A171776 A277401 A208874

Adjacent sequences: A066261 A066262 A066263 * A066265 A066266 A066267

Keyword

nonn

Author

Patrick De Geest, Dec 10 2001

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

Status

approved