A369251 Numbers that have at least one representation as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.

27, 39, 51, 55, 71, 75, 87, 91, 95, 103, 111, 119, 123, 131, 135, 147, 151, 155, 167, 183, 187, 191, 195, 199, 203, 211, 215, 231, 239, 247, 251, 255, 263, 267, 271, 275, 287, 291, 299, 311, 315, 327, 331, 335, 343, 351, 355, 359, 363, 371, 375, 383, 391, 395, 407, 411, 419, 423, 431, 435, 439, 447, 451, 455, 459

Offset: 1

Author

Antti Karttunen, Jan 22 2024

Keywords

• nonn

Comments

By necessity all terms are of the form 4m+3 (in A004767).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Complement of A369464.

Sequence A369252 sorted into ascending order, with duplicates removed.

Setwise difference A004767 \ A369056.

Subsequence of A239433.

Cf. A369054, A369055.

Cf. A369250 (primes in this sequence).

Programs

PARI

isA369251(n) = if(3!=(n%4),0, my(v = [3,3], ip = #v, r); while(1, r = (n-(v[1]*v[2])) / (v[1]+v[2]); if(r < v[2], ip--, ip = #v; if(1==denominator(r) && isprime(r), return(1))); if(!ip, return(0)); v[ip] = nextprime(1+v[ip]); for(i=1+ip,#v,v[i]=v[i-1])));

Formula

{k | A369054(k) > 0}.