OFFSET
1,6
COMMENTS
From Jaroslav Krizek, Feb 18 2010: (Start)
Number of divisors d of number n such that d divides sigma(n).
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
See program.
EXAMPLE
For n = 12: a(12) = 3; sigma(12) = 28, divisors of 12: 1, 2, 3, 4, 6, 12; d divides sigma(n) for 3 divisors d: 1, 2, 4.
n=96: D[96]={1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96}, D[sigma(96)]={1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252}, NCD[n, sigma(n)]={1, 2, 3, 4, 6, 12} so a(96)=6.
MATHEMATICA
g1[x_] := Divisors[x] g2[x_] := Divisors[DivisorSigma[1, x]] ncd[x_] := Length[Intersection[g1[x], g2[x]]] Table[ncd[w], {w, 1, 128}]
Table[Length[Intersection[Divisors[n], Divisors[DivisorSigma[1, n]]]], {n, 100}] (* Vincenzo Librandi, Oct 09 2017 *)
PROG
(PARI) a(n)=numdiv(gcd(sigma(n), n)) \\ Charles R Greathouse IV, Mar 09 2014
(Magma) [NumberOfDivisors(GCD(SumOfDivisors(n), n)): n in [1..100]]; // Vincenzo Librandi, Oct 09 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 13 2002
STATUS
approved