A176256 Numbers of the form 4k+1 with least prime divisor of the form 4m-1.

9, 21, 33, 45, 49, 57, 69, 77, 81, 93, 105, 117, 121, 129, 133, 141, 153, 161, 165, 177, 189, 201, 209, 213, 217, 225, 237, 249, 253, 261, 273, 285, 297, 301, 309, 321, 329, 333, 341, 345, 357, 361, 369, 381, 393, 405, 413, 417, 429, 437, 441, 453, 465, 469

Offset: 1

Author

Vladimir Shevelev, Apr 13 2010

Keywords

• nonn

Comments

By definition, all terms are composite numbers.

Cannot be the hypotenuse of a primitive Pythagorean triangle. - Robert G. Wilson v, Mar 16 2014

Links

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

Crossrefs

Cf. A176255, A002148, A002145, A016813, A004767.

Complement of A020882 in 1 == Mod 4.

Programs

Mathematica

fQ[n_] := Mod[ n, 4] == 1 && Mod[ FactorInteger[n][[1, 1]], 4] == 3; Select[Range@470, fQ] (* Robert G. Wilson v, Apr 08 2014 *)

PARI

isok(n) = ((n % 4) == 1) && (f = factor(n)) && ((f[1, 1] % 4) == 3); \\ Michel Marcus, Mar 16 2014

Extensions

More terms from Michel Marcus, Mar 16 2014