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A072202 Same numbers of prime factors of forms 4*k+1 and 4*k+3, counted with multiplicity. 8
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 (list; graph; refs; listen; history; text; internal format)
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 * A275474 A076351 A140117

Adjacent sequences:  A072199 A072200 A072201 * A072203 A072204 A072205

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 03 2002

STATUS

approved

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Last modified May 19 10:36 EDT 2019. Contains 323390 sequences. (Running on oeis4.)