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
Keywords
Examples
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.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Crossrefs
Cf. A128830.
Programs
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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
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Mathematica
pdc[n_]:=Module[{s=DivisorSigma[1,n]},Count[Divisors[n],?(CoprimeQ[ #,s]&)]]; Array[pdc,110] (* _Harvey P. Dale, Jul 16 2016 *) -
PARI
a(n)=my(s=sigma(n));sumdiv(n,d,gcd(s,d)==1) \\ Charles R Greathouse IV, Feb 19 2013
Extensions
More terms from Emeric Deutsch, May 05 2007
Comments