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A001826 Number of divisors of n of form 4k+1. 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Not multiplicative: a(21) <> a(3)*a(7), for example. - R. J. Mathar, Sep 15 2015

LINKS

Nick Hobson, Table of n, a(n) for n = 1..10000

Michael Gilleland, Some Self-Similar Integer Sequences

FORMULA

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

MAPLE

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

MATHEMATICA

a[n_] := Count[Divisors[n], d_ /; Mod[d, 4] == 1]; Table[a[n], {n, 1, 105}] (* Jean-Fran├žois Alcover, Nov 26 2013 *)

PROG

(PARI) a(n)=if(n<1, 0, sumdiv(n, d, d%4==1))

CROSSREFS

Cf. A001842.

Sequence in context: A318324 A317934 A279848 * A003641 A165190 A025890

Adjacent sequences:  A001823 A001824 A001825 * A001827 A001828 A001829

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Better definition from Michael Somos, Apr 26 2004

STATUS

approved

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Last modified October 22 09:57 EDT 2018. Contains 316433 sequences. (Running on oeis4.)