A004622 Divisible only by primes congruent to 4 mod 7.

1, 11, 53, 67, 109, 121, 137, 151, 179, 193, 263, 277, 347, 389, 431, 487, 557, 571, 583, 599, 613, 641, 683, 737, 739, 809, 823, 907, 977, 991, 1019, 1033, 1061, 1103, 1117, 1187, 1199, 1201, 1229, 1327, 1331, 1439, 1453, 1481, 1507, 1523, 1579, 1607, 1621

Offset

1,2

Comments

a(1) = 1 is included by convention (all the primes that divide 1 are congruent to 4 mod 7).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Mathematica

ok[1]=True; ok[n_]:=And@@(Mod[#, 7]==4&)/@FactorInteger[n][[All, 1]]; Select[Range[5000], ok] (* Vincenzo Librandi, Aug 20 2012 *)
Join[{1}, Select[Range[2000], Union[Mod[FactorInteger[#][[;; , 1]], 7]]=={4}&]] (* Harvey P. Dale, May 04 2023 *)

Prog

(Magma) [n: n in [1..2000] | forall{d: d in PrimeDivisors(n) | d mod 7 eq 4}]; // Vincenzo Librandi, Aug 20 2012

Crossrefs

Sequence in context: A191099 A325727 A370502 * A045471 A086715 A178453

Adjacent sequences: A004619 A004620 A004621 * A004623 A004624 A004625

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Offset changed from 0 to 1 by Vincenzo Librandi, Aug 20 2012

Missing a(41) added by Sean A. Irvine, Jun 08 2016

Status

approved