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%I #19 Jan 01 2020 21:52:57
%S 1,2,2,3,2,1,2,4,3,2,2,2,2,2,2,5,2,2,2,2,4,2,2,1,3,2,4,1,2,2,2,6,2,2,
%T 4,9,2,2,4,1,2,2,2,2,2,2,2,2,3,6,2,2,2,1,4,2,4,2,2,2,2,2,6,7,4,2,2,2,
%U 2,4,2,4,2,2,6,2,4,2,2,2,5,2,2,2,4,2,2,2,2,2,2,2,4,2,2,1,2,6,2,9,2,2,2,2,4
%N a(n) = the number of positive divisors of n which are coprime to sigma(n) = A000203(n).
%C In the first 1000 terms, only 69 are odd. - _Harvey P. Dale_, Jul 16 2016
%H Harvey P. Dale, <a href="/A116199/b116199.txt">Table of n, a(n) for n = 1..1000</a>
%e The sum of the positive divisors of 12 is 1+2+3+4+6+12 = 28. There are 2 positive divisors (1 and 3) of 12 which are coprime to 28. So a(12) = 2.
%p with(numtheory): a:=proc(n) local div,ct,j: div:=divisors(n): ct:=0: for j from 1 to tau(n) do if igcd(div[j],sigma(n))=1 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(a(n),n=1..140); # _Emeric Deutsch_, May 05 2007
%t pdc[n_]:=Module[{s=DivisorSigma[1,n]},Count[Divisors[n],_?(CoprimeQ[ #,s]&)]]; Array[pdc,110] (* _Harvey P. Dale_, Jul 16 2016 *)
%o (PARI) a(n)=my(s=sigma(n));sumdiv(n,d,gcd(s,d)==1) \\ _Charles R Greathouse IV_, Feb 19 2013
%Y Cf. A128830.
%K nonn
%O 1,2
%A _Leroy Quet_, Apr 16 2007
%E More terms from _Emeric Deutsch_, May 05 2007
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