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Number of composites < primorial(p) with all prime factors > p.
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%I #15 Apr 04 2019 17:25:54

%S 0,0,0,5,141,2517,49835,1012858,24211837,721500293,22627459400,

%T 844130935667,34729870646917,1491483322755273,69890000837179156

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

%C 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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Primorial.html">Primorial</a>

%F a(n) = n + A005867(n) - A000849(n) - 1. - _Michael De Vlieger_, Apr 03 2019, citing Dennis Martin's comment above.

%e 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).

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

%Y Cf. A000849, A002110, A005867.

%K nonn

%O 1,4

%A _Patrick De Geest_, Dec 10 2001

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

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

%E a(14)-a(15) from _Donovan Johnson_, May 03 2010