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%I #12 Feb 03 2019 07:05:49
%S 1,1,2,3,2,2,2,1,1,2,2,1,2,2,4,5,2,1,2,2,4,2,2,2,3,2,4,2,2,4,2,1,4,2,
%T 4,3,2,2,4,2,2,4,2,2,2,2,2,2,3,3,4,2,2,4,4,2,4,2,2,2,2,2,2,7,4,4,2,2,
%U 4,4,2,1,2,2,3,2,4,4,2,1,5,2,2,2,4,2,4,2,2,2,4,2,4,2,4,1,2,3,2,9,2,4,2,2,8
%N a(n) = the number of positive divisors of n which are coprime to d(n), where d(n) = the number of positive divisors of n.
%H Harvey P. Dale, <a href="/A128830/b128830.txt">Table of n, a(n) for n = 1..1000</a>
%e The 6 positive divisors of 20 are 1,2,4,5,10,20. Of these, only 1 and 5 are coprime to d(20) = 6. So a(20) = 2.
%p with(numtheory): a:=proc(n) local div,ct,i: div:=divisors(n): ct:=0: for i from 1 to tau(n) do if igcd(div[i],tau(n))=1 then ct:=ct+1 else ct:=ct: fi od: ct; end: seq(a(n),n=1..140); # _Emeric Deutsch_, Apr 14 2007
%t cpd[n_]:=Module[{ds=DivisorSigma[0,n]},Count[Divisors[n],_?(CoprimeQ[ #,ds]&)]]; Array[cpd,110] (* _Harvey P. Dale_, Apr 21 2012 *)
%K nonn
%O 1,3
%A _Leroy Quet_, Apr 13 2007
%E More terms from _Emeric Deutsch_, Apr 14 2007