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

1,2

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.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Pierpont Prime.

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A005109, A048737, A122254, A122261.

Sequence in context: A031995 A023752 A048737 * A122254 A249626 A102823

Adjacent sequences: A122257 A122258 A122259 * A122261 A122262 A122263

Keyword

nonn,easy

Author

Reinhard Zumkeller, Aug 29 2006

Status

approved