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A173438 Number of divisors d of number n such that d does not divide sigma(n). 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A103493 A121480 A082601

Adjacent sequences:  A173435 A173436 A173437 * A173439 A173440 A173441

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Feb 18 2010

STATUS

approved

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Last modified February 18 05:30 EST 2019. Contains 320245 sequences. (Running on oeis4.)