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

1,2

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

Links

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

Example

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

Mathematica

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

Prog

(Haskell)
a072202 n = a072202_list !! (n-1)
a072202_list = [x | x <- [1..], a083025 x == a065339 x]
-- Reinhard Zumkeller, Jan 10 2012
(Scheme) (define A072202 (ZERO-POS 1 1 A079635)) ;; [requires also my IntSeq-library] - Antti Karttunen, Feb 03 2016
(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

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.

Sequence in context: A084561 A277166 A078613 * A354189 A275474 A354192

Adjacent sequences: A072199 A072200 A072201 * A072203 A072204 A072205

Keyword

nonn

Author

Reinhard Zumkeller, Jul 03 2002

Status

approved