A376543 Numbers of the form p^e * q^f with p, q distinct primes = 3 mod 4 and e and f both odd.

21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, 189, 201, 209, 213, 217, 237, 249, 253, 297, 301, 309, 321, 329, 341, 381, 393, 413, 417, 437, 453, 469, 473, 489, 497, 501, 513, 517, 537, 553, 573, 581, 589, 597, 621, 633, 649, 669, 681, 713, 717, 721, 737, 749, 753, 781, 789

Offset

1,1

Comments

Murru & Salvatori refer to these as Blum integers, though that title properly rests with A016105.

Links

Table of n, a(n) for n=1..57.

Nadir Murru and Giulia Salvatori, Integer factorization via continued fractions and quadratic forms, arXiv preprint (2024). arXiv:2409.03486 [math.NT]

Prog

(PARI) list(lim)=my(P=List(), v=List(), t, p); forstep(e=1, logint(lim\=1, 3), 2, forprimestep(p=3, sqrtnint(lim\3, e), 4, listput(P, p^e))); P=Set(P); for(i=2, #P, p=P[i]; for(j=1, i-1, t=p*P[j]; if(t>lim, break); if(gcd(p, P[j])==1, listput(v, t)))); Set(v)

Crossrefs

A016105 is a subsequence. Subsequence of A007774.

Sequence in context: A190299 A280262 A084109 * A016105 A187073 A271101

Adjacent sequences: A376540 A376541 A376542 * A376544 A376545 A376546

Keyword

nonn

Author

Charles R Greathouse IV, Sep 26 2024

Status

approved