A187811 Numbers having at least one prime factor of form 4*k+3.

3, 6, 7, 9, 11, 12, 14, 15, 18, 19, 21, 22, 23, 24, 27, 28, 30, 31, 33, 35, 36, 38, 39, 42, 43, 44, 45, 46, 47, 48, 49, 51, 54, 55, 56, 57, 59, 60, 62, 63, 66, 67, 69, 70, 71, 72, 75, 76, 77, 78, 79, 81, 83, 84, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99

Offset: 1

Author

Reinhard Zumkeller, Jan 07 2013

Keywords

• nonn

Comments

A005091(a(n)) > 0. - Reinhard Zumkeller, Jan 07 2013

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A072437 (complement); A002145, A009003.

Programs

Haskell

import Data.List (findIndices)
a187811 n = a187811_list !! (n-1)
a187811_list = map (+ 1) $ findIndices (> 0) a005091_list
-- Reinhard Zumkeller, Jan 07 2013

Mathematica

pfQ[n_]:=AnyTrue[Transpose[FactorInteger[n]][[1]],Mod[#,4]==3&]; Select[ Range[100],pfQ] (* The program uses the AnyTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 26 2016 *)

PARI

is(n)=if(n%4==3,return(1)); my(f=factor(n)[,1]%4); for(i=1,#f, if(f[i]==3, return(1))); 0 \\ Charles R Greathouse IV, Sep 01 2015

Formula

a(n) ~ n. - Charles R Greathouse IV, Sep 01 2015