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A001826
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Number of divisors of n of form 4k+1.
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14
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1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 1, 3, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 4, 1, 1, 1, 2, 3, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 3, 1, 4, 2, 1, 2, 2, 2, 1, 2, 2, 2, 3, 1, 2, 2, 1, 2, 3, 2, 1, 2, 4, 1, 2, 1, 2, 4, 2, 1, 2, 1, 2, 1, 2, 2, 3, 3, 2, 2, 1, 2, 4
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OFFSET
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1,5
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COMMENTS
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Not multiplicative: a(21) <> a(3)*a(7), for example. - R. J. Mathar, Sep 15 2015
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LINKS
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Nick Hobson, Table of n, a(n) for n = 1..10000
Michael Gilleland, Some Self-Similar Integer Sequences
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FORMULA
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G.f.: Sum_{n>0} x^n/(1-x^(4n)) = Sum x^(4n+1)/(1-x^(4n+1)), n=0..inf.
a(n) = A001227(n) - A001842(n). - Reinhard Zumkeller, Apr 18 2006
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MAPLE
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d:=proc(r, m, n) local i, t1; t1:=0; for i from 1 to n do if n mod i = 0 and i-r mod m = 0 then t1:=t1+1; fi; od: t1; end; # no. of divisors i of n with i == r mod m
A001826 := proc(n)
add(`if`(modp(d, 4)=1, 1, 0), d=numtheory[divisors](n)) ;
end proc: # R. J. Mathar, Sep 15 2015
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MATHEMATICA
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a[n_] := Count[Divisors[n], d_ /; Mod[d, 4] == 1]; Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Nov 26 2013 *)
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PROG
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(PARI) a(n)=if(n<1, 0, sumdiv(n, d, d%4==1))
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CROSSREFS
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Cf. A001842.
Sequence in context: A318324 A317934 A279848 * A003641 A165190 A025890
Adjacent sequences: A001823 A001824 A001825 * A001827 A001828 A001829
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Better definition from Michael Somos, Apr 26 2004
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STATUS
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approved
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