A116199 a(n) = the number of positive divisors of n which are coprime to sigma(n) = A000203(n).

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, 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, 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

Offset

1,2

Comments

In the first 1000 terms, only 69 are odd. - Harvey P. Dale, Jul 16 2016

Links

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

Example

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.

Maple

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

Mathematica

pdc[n_]:=Module[{s=DivisorSigma[1, n]}, Count[Divisors[n], _?(CoprimeQ[ #, s]&)]]; Array[pdc, 110] (* Harvey P. Dale, Jul 16 2016 *)

Prog

(PARI) a(n)=my(s=sigma(n)); sumdiv(n, d, gcd(s, d)==1) \\ Charles R Greathouse IV, Feb 19 2013

Crossrefs

Cf. A128830.

Sequence in context: A044050 A096826 A346010 * A369031 A162915 A359791

Adjacent sequences: A116196 A116197 A116198 * A116200 A116201 A116202

Keyword

nonn

Author

Leroy Quet, Apr 16 2007

Extensions

More terms from Emeric Deutsch, May 05 2007

Status

approved