

A319049


Primes p such that none of p  1, p  2 and p  3 are squarefree.


3



101, 127, 353, 727, 1277, 1423, 1451, 1667, 2153, 2351, 2647, 3187, 3251, 3511, 3701, 3719, 3727, 4421, 4951, 5051, 5393, 5527, 6427, 6653, 6959, 7517, 7867, 8527, 9127, 9551, 9803, 9851, 10243, 10253, 10487, 10831, 11273, 11351, 11777, 11827, 12007, 12251, 12277
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OFFSET

1,1


COMMENTS

If p is a term, so that there are primes q,r,s such that q^2p3, r^2p2 and s^2p1, then the sequence includes all primes == p (mod q^2*r^2*s^2). In particular, the sequence is infinite, and a(n)/(n*log(n)) is bounded above and below by constants.  Robert Israel, Sep 09 2018


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000


EXAMPLE

98 = 2*7^2, 99 = 3^2*11 and 100 = 2^2*5^2. So 101 is a term.


MAPLE

Res:= NULL: count:= 0:
p:= 1;
while count < 100 do
p:= nextprime(p);
if not ormap(numtheory:issqrfree, [p1, p2, p3]) then
count:= count+1; Res:= Res, p
fi
od:
Res; # Robert Israel, Sep 09 2018


MATHEMATICA

Select[Prime[Range[2000]], !SquareFreeQ[#  1] && !SquareFreeQ[#  2] && !SquareFreeQ[#  3]&] (* JeanFrançois Alcover, Sep 17 2018 *)


PROG

(PARI) isok(p) = isprime(p) && !issquarefree(p1) && !issquarefree(p2) && !issquarefree(p3); \\ Michel Marcus, Sep 09 2018
(MAGMA) [p: p in PrimesUpTo(13000)  not IsSquarefree(p1) and not IsSquarefree(p2) and not IsSquarefree(p3)]; // Vincenzo Librandi, Sep 17 2018


CROSSREFS

Cf. A000040, A039787, A049231, A240473, A257545, A318959.
Sequence in context: A095635 A060916 A075793 * A052086 A154270 A056730
Adjacent sequences: A319046 A319047 A319048 * A319050 A319051 A319052


KEYWORD

nonn


AUTHOR

Seiichi Manyama, Sep 08 2018


STATUS

approved



