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

1,1

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A259766 A273937 A326257 * A231275 A158725 A090825

Adjacent sequences: A387213 A387214 A387215 * A387217 A387218 A387219

Keyword

nonn

Author

Michel Marcus, Aug 22 2025

Status

approved