A078613 Same numbers of distinct prime factors of forms 4*k+1 and 4*k+3.

1, 2, 4, 8, 15, 16, 30, 32, 35, 39, 45, 51, 55, 60, 64, 70, 75, 78, 87, 90, 91, 95, 102, 110, 111, 115, 117, 119, 120, 123, 128, 135, 140, 143, 150, 153, 155, 156, 159, 174, 175, 180, 182, 183, 187, 190, 203, 204, 215, 219, 220, 222, 225, 230, 234, 235, 238, 240

Offset: 1

Author

Reinhard Zumkeller, Dec 10 2002

Keywords

• nonn

Comments

Equivalently, numbers n such that A005089(n)=A005091(n); A005094(a(n))=0.

A001221(a(n)) and a(n) are of opposite parity.

If m is in the sequence, then also 2*m.

Conjecture : a(n) is asymptotic to c*n where c is around 4 - Benoit Cloitre, Jan 06 2003

Examples

			n = 99 = [(4*0+3)^2]*[(4*1+1)], therefore 99 is a term.
		

Links

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

Crossrefs

Cf. A072202.

Cf. A221264, A221265.

Programs

Haskell

a078613 n = a078613_list !! (n-1)
a078613_list = filter ((== 0) . a005094) [1..]
-- Reinhard Zumkeller, Jan 07 2013

Mathematica

fQ[n_]:=Plus@@((Mod[#[[1]],4]-2)&/@If[n==1,{},FactorInteger[n]])==0; Select[Range[240],fQ] (* Ray Chandler, Dec 18 2011*)

Extensions

Edited by Ray Chandler, Dec 18 2011