

A122260


Multiplicative closure of Pierpont primes.


5



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
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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/(p1) = 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



