A122260 Multiplicative closure of Pierpont primes.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, 32, 34, 35, 36, 37, 38, 39, 40, 42, 45, 48, 49, 50, 51, 52, 54, 56, 57, 60, 63, 64, 65, 68, 70, 72, 73, 74, 75, 76, 78, 80, 81, 84, 85, 90, 91, 95, 96, 97, 98, 100, 102, 104, 105, 108

Offset: 1

Author

Reinhard Zumkeller, Aug 29 2006

Keywords

• nonn
• easy

Comments

If u and v are terms then also u*v is a term; A005109 is the generating subsequence;

A122261(a(n)) = 1;

A122254 is a subsequence: a(n) = A122254(n) = A048737(n) for n < 22.

Examples

			15 = 3 * 5 is a term since both 3 and 5 are Pierpont primes.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pierpont Prime.

Crossrefs

Cf. A005109, A048737, A122254, A122261.

Programs

Mathematica

mx = 108; Select[Range@mx, Complement[FactorInteger[#][[All, 1]], Select[Prime@Range@mx, Max[FactorInteger[# - 1][[All, 1]]] < 5 &], {1}] == {} &] (* Ivan Neretin, Aug 13 2015 *)

PARI

sm3(n)=n>>=valuation(n,2);n==3^valuation(n,3)
is(n)=my(f=factor(n)[,1]);for(i=1,#f,if(!sm3(f[i]),return(0)));1 \\ Charles R Greathouse IV, Feb 21 2013

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A005109} p/(p-1) = 5.80109266072985445612... - Amiram Eldar, Sep 27 2020