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A066264
Number of composites < primorial(p) with all prime factors > p.
0
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
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
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