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

1,4

Comments

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

Links

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

Formula

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

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A286957 A195017 A078806 * A376701 A103493 A121480

Adjacent sequences: A173435 A173436 A173437 * A173439 A173440 A173441

Keyword

nonn

Author

Jaroslav Krizek, Feb 18 2010

Status

approved