A128830 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.

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, 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, 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

Offset: 1

Author

Leroy Quet, Apr 13 2007

Keywords

• nonn

Examples

			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.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Maple

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

Mathematica

cpd[n_]:=Module[{ds=DivisorSigma[0,n]},Count[Divisors[n],?(CoprimeQ[ #,ds]&)]]; Array[cpd,110] (* _Harvey P. Dale, Apr 21 2012 *)

Extensions

More terms from Emeric Deutsch, Apr 14 2007