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 A001826 Number of divisors of n of the 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_{n>=0} x^(4n+1)/(1-x^(4n+1)). 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-François Alcover, Nov 26 2013 *) PROG (PARI) a(n)=if(n<1, 0, sumdiv(n, d, d%4==1)) CROSSREFS Cf. A001842. Sequence in context: A317934 A353376 A279848 * A003641 A355241 A165190 Adjacent sequences:  A001823 A001824 A001825 * A001827 A001828 A001829 KEYWORD nonn AUTHOR EXTENSIONS Better definition from Michael Somos, Apr 26 2004 STATUS approved

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Last modified July 2 12:39 EDT 2022. Contains 355004 sequences. (Running on oeis4.)