A072202 Same numbers of prime factors of forms 4*k+1 and 4*k+3, counted with multiplicity.

1, 2, 4, 8, 15, 16, 30, 32, 35, 39, 51, 55, 60, 64, 70, 78, 87, 91, 95, 102, 110, 111, 115, 119, 120, 123, 128, 140, 143, 155, 156, 159, 174, 182, 183, 187, 190, 203, 204, 215, 219, 220, 222, 225, 230, 235, 238, 240, 246, 247, 256, 259, 267, 280, 286, 287, 291

Offset: 1

Author

Reinhard Zumkeller, Jul 03 2002

Keywords

• nonn

Comments

Equivalently, numbers n such that A083025(n) = A065339(n), indices of zeros in A079635.

Closed under multiplication.

Closed with respect to permutation A267099. - Antti Karttunen, Feb 03 2016

Examples

			825 = 3*5*5*11 = [(4*0+3)*(4*2+3)]*[(4*1+1)*(4*1+1)], therefore 825 is a term.
		

Links

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

Crossrefs

Cf. A002144, A002145, A202237 (odd elements), A079635, A065339, A083025, A267099.

Primitive elements are {2} U A080774. - Franklin T. Adams-Watters, Dec 16 2011.

Subsequence of A078613 and of A268381.

Programs

Haskell

a072202 n = a072202_list !! (n-1)
a072202_list = [x | x <- [1..], a083025 x == a065339 x]
-- Reinhard Zumkeller, Jan 10 2012

Mathematica

f[n_]:=Plus@@Last/@Select[If[==1,{},FactorInteger[n]],Mod[#[[1]],4]==1&]; Table[f[n],{n,100}] (* Ray Chandler, Dec 18 2011 *)

PARI

isok(n) = {my(f = factor(n)); sum(k=1, #f~, ((f[k,1] % 4)==1)*f[k,2]) == sum(k=1, #f~, ((f[k,1] % 4)==3)*f[k,2]);} \\ Michel Marcus, Feb 05 2016

Scheme

(define A072202 (ZERO-POS 1 1 A079635)) ;; [requires also my IntSeq-library] - Antti Karttunen, Feb 03 2016