A072437 Numbers with no prime factors of form 4*k+3.

1, 2, 4, 5, 8, 10, 13, 16, 17, 20, 25, 26, 29, 32, 34, 37, 40, 41, 50, 52, 53, 58, 61, 64, 65, 68, 73, 74, 80, 82, 85, 89, 97, 100, 101, 104, 106, 109, 113, 116, 122, 125, 128, 130, 136, 137, 145, 146, 148, 149, 157, 160, 164, 169, 170, 173, 178, 181, 185, 193, 194

Offset: 1

Author

Reinhard Zumkeller, Jun 17 2002

Keywords

• nonn

Comments

m is a term iff A072436(m) = m.

These numbers have density zero (Pollack).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• P. Pollack, Analytic and Combinatorial Number Theory Course Notes, p. 119. alternate link

Crossrefs

Cf. A004144, A002144, A002145, A004613 (odd terms).

A097706(a(n)) = 1.

Cf. A187811 (complement).

Programs

Haskell

import Data.List (elemIndices)
a072437 n = a072437_list !! (n-1)
a072437_list = map (+ 1) $ elemIndices 0 a005091_list
-- Reinhard Zumkeller, Jan 07 2013

Mathematica

npfQ[n_]:=Count[Transpose[FactorInteger[n]][[1]],?(Mod[#,4]==3&)]==0; Select[Range[200],npfQ] (* _Harvey P. Dale, Nov 12 2013 *)

PARI

is(n)=n==1||vecmax(factor(n)[,1]%4)<3 \\ Charles R Greathouse IV, Apr 16 2012

Formula

n>0 such that A001842(n)=0. - Benoit Cloitre, Apr 24 2003

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

A065339(a(n)) = 0 . - R. J. Mathar, Jan 28 2025