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A173438 Number of divisors d of number n such that d does not divide sigma(n).

%I A173438 #16 Oct 09 2017 00:05:02
%S A173438 0,1,1,2,1,0,1,3,2,2,1,3,1,2,2,4,1,4,1,4,3,2,1,2,2,2,3,0,1,4,1,5,2,2,
%T A173438 3,8,1,2,3,4,1,4,1,3,4,2,1,7,2,5,2,4,1,4,3,4,3,2,1,6,1,2,5,6,3,4,1,4,
%U A173438 2,6,1,10,1,2,5,3,3,4,1,8,4,2,1,6,3,2,2,5,1,6,2,3,3,2,2,6,1,5
%N A173438 Number of divisors d of number n such that d does not divide sigma(n).
%C A173438 a(n) = 0 for multiply-perfect numbers (A007691).
%H A173438 Antti Karttunen, <a href="/A173438/b173438.txt">Table of n, a(n) for n = 1..20000</a>
%F A173438 a(n) = A000005(n) - A073802(n).
%F A173438 a(n) = tau(n) - tau(gcd(n,sigma(n))). - _Antti Karttunen_, Oct 08 2017
%e A173438 For n = 12, a(12) = 3; sigma(12) = 28, divisors of 12: 1, 2, 3, 4, 6, 12; d does not divide sigma(n) for 3 divisors d: 3, 6 and 12.
%p A173438 A173438 := proc(n)
%p A173438     local sd,a;
%p A173438     sd := numtheory[sigma](n) ;
%p A173438     a := 0 ;
%p A173438     for d in numtheory[divisors](n) do
%p A173438         if modp(sd,d) <> 0 then
%p A173438             a := a+1 ;
%p A173438         end if;
%p A173438     end do:
%p A173438     a;
%p A173438 end proc: # _R. J. Mathar_, Oct 26 2015
%t A173438 Table[DivisorSum[n, 1 &, ! Divisible[DivisorSigma[1, n], #] &], {n, 98}] (* _Michael De Vlieger_, Oct 08 2017 *)
%o A173438 (PARI) A173438(n) = (numdiv(n) - numdiv(gcd(sigma(n), n))); \\ (See PARI-code in A073802) - _Antti Karttunen_, Oct 08 2017
%Y A173438 Cf. A000005, A000203, A007691, A009194, A073802, A286570.
%K A173438 nonn
%O A173438 1,4
%A A173438 _Jaroslav Krizek_, Feb 18 2010