login
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.
2
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
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
KEYWORD
nonn
AUTHOR
Leroy Quet, Apr 13 2007
EXTENSIONS
More terms from Emeric Deutsch, Apr 14 2007
STATUS
approved