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

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, 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, 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

Offset: 1

Author

Jaroslav Krizek, Feb 18 2010

Keywords

• nonn

Comments

a(n) = 0 for multiply-perfect numbers (A007691).

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000005, A000203, A007691, A009194, A073802, A286570.

Programs

Maple

A173438 := proc(n)
    local sd,a;
    sd := numtheory[sigma](n) ;
    a := 0 ;
    for d in numtheory[divisors](n) do
        if modp(sd,d) <> 0 then
            a := a+1 ;
        end if;
    end do:
    a;
end proc: # R. J. Mathar, Oct 26 2015

Mathematica

Table[DivisorSum[n, 1 &, ! Divisible[DivisorSigma[1, n], #] &], {n, 98}] (* Michael De Vlieger, Oct 08 2017 *)

PARI

A173438(n) = (numdiv(n) - numdiv(gcd(sigma(n), n))); \\ (See PARI-code in A073802) - Antti Karttunen, Oct 08 2017

Formula

a(n) = A000005(n) - A073802(n).

a(n) = tau(n) - tau(gcd(n,sigma(n))). - Antti Karttunen, Oct 08 2017