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A078613
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Same numbers of distinct prime factors of forms 4*k+1 and 4*k+3.
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6
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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n = 99 = [(4*0+3)^2]*[(4*1+1)], therefore 99 is a term.
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MATHEMATICA
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fQ[n_]:=Plus@@((Mod[#[[1]], 4]-2)&/@If[n==1, {}, FactorInteger[n]])==0; Select[Range[240], fQ] (* Ray Chandler, Dec 18 2011*)
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PROG
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(Haskell)
a078613 n = a078613_list !! (n-1)
a078613_list = filter ((== 0) . a005094) [1..]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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