A387216 Numbers that have at least two prime factors (counting multiplicity) congruent to 1 mod 3.

49, 91, 98, 133, 147, 169, 182, 196, 217, 245, 247, 259, 266, 273, 294, 301, 338, 343, 361, 364, 392, 399, 403, 427, 434, 441, 455, 469, 481, 490, 494, 507, 511, 518, 532, 539, 546, 553, 559, 588, 589, 602, 637, 651, 665, 676, 679, 686, 703, 721, 722, 728, 735, 741, 763, 777, 784, 793, 798

Offset: 1

Author

Michel Marcus, Aug 22 2025

Keywords

• nonn
• new

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..7923
• Hajrudin Fejzić, Nontrivial Solutions to a Cubic Identity and the Factorization of n^2+n+1, arXiv:2508.14937 [math.GM], 2025. See Theorem 2 p. 4.

Crossrefs

Cf. A002476 (primes congruent to 1 mod 3), A050931 (at least one).

Programs

Magma

res := [];for n in [1..1000] do L := [ f[2] : f in Factorization(n) | f[1] mod 3 eq 1 ]; count := (#L eq 0) select 0 else &+L;if count gt 1 then Append(~res, n); end if; end for; res;
 // Vincenzo Librandi, Aug 24 2025

Mathematica

ff[{m_,n_}]:=Table[m,n];Select[Range[798],Count[Mod[ff/@FactorInteger[#]//Flatten,3],1]>1&] (* James C. McMahon, Aug 22 2025 *)

PARI

isok(k) = my(f=factor(k)); sum(i=1, #f~, if ((f[i,1]%3) == 1, f[i,2])) >= 2;