

A319386


Semiprimes k = pq with primes p < q such that p1 does not divide q1.


2



35, 55, 77, 95, 115, 119, 143, 155, 161, 187, 203, 209, 215, 221, 235, 247, 253, 287, 295, 299, 319, 323, 329, 335, 355, 371, 377, 391, 395, 403, 407, 413, 415, 437, 473, 493, 497, 515, 517, 527, 533, 535, 551, 559, 581, 583, 589, 611, 623, 629, 635, 649, 655, 667, 689, 695, 697, 707, 713, 731
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OFFSET

1,1


COMMENTS

The "antiCarmichael semiprimes" defined: semiprimes k such that lpf(k)1 does not divide k1; then also gpf(k)1 does not divide k1.
All the terms are odd and indivisible by 3.
If k is in the sequence, then gcd(k,b^kb)=1 for some integer b.
These numbers are probably all semiprimes in A121707.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


EXAMPLE

35 = 5*7 is a term since 51 does not divide 71.
35 is a term since lpf(35)1 = 51 does not divide 351.


MAPLE

N:= 1000: # for terms <= N
P:= select(isprime, {seq(i, i=5..N/5, 2)}):
S:= {}:
for p in P do
Qs:= select(q > q > p and q <= N/p and (q1 mod (p1) <> 0), P);
S:= S union map(`*`, Qs, p);
od:
sort(convert(S, list)); # Robert Israel, Apr 14 2020


PROG

(PARI) isok(n) = {if ((bigomega(n) == 2) && (omega(n) == 2), my(p = factor(n)[1, 1], q = factor(n)[2, 1]); (q1) % (p1) != 0; ); } \\ Michel Marcus, Sep 18 2018
(PARI) list(lim)=my(v=List(), s=sqrtint(lim\=1)); forprime(q=7, lim\5, forprime(p=5, min(min(q2, s), lim\q), if((q1)%(p1), listput(v, p*q)))); Set(v) \\ Charles R Greathouse IV, Apr 14 2020


CROSSREFS

Subsequence of A046388.
Complement of A162730 w.r.t. A006881.
Cf. A001358, A121707.
Sequence in context: A335902 A121707 A267999 * A157352 A176255 A090877
Adjacent sequences: A319383 A319384 A319385 * A319387 A319388 A319389


KEYWORD

nonn


AUTHOR

Thomas Ordowski, Sep 18 2018


STATUS

approved



