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A173438
Number of divisors d of number n such that d does not divide sigma(n).
5
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
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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Feb 18 2010
STATUS
approved