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

1,3

Links

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

Example

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.

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 *)

Crossrefs

Sequence in context: A286657 A334052 A160570 * A090387 A030329 A300139

Adjacent sequences: A128827 A128828 A128829 * A128831 A128832 A128833

Keyword

nonn

Author

Leroy Quet, Apr 13 2007

Extensions

More terms from Emeric Deutsch, Apr 14 2007

Status

approved