|
|
A073808
|
|
Number of common divisors of sigma_1(n) and sigma_2(n).
|
|
5
|
|
|
1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 2, 8, 3, 2, 2, 4, 2, 2, 6, 4, 2, 3, 2, 4, 3, 2, 3, 4, 2, 4, 3, 4, 2, 3, 2, 8, 4, 2, 2, 4, 4, 4, 3, 4, 2, 6, 3, 4, 6, 4, 2, 12, 2, 2, 4, 2, 3, 3, 2, 8, 3, 3, 2, 4, 2, 2, 4, 4, 3, 3, 2, 4, 3, 2, 2, 6, 3, 2, 6, 4, 2, 4, 3, 8, 3, 2, 3, 8, 2, 4, 4, 4, 2, 3, 2, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
a(n) = Card[Intersection[D[A000203(n)], D[A001157(n)]]]. - This is the formula given by the original author. D[x] here means the set of divisors of x. - Antti Karttunen, Nov 23 2017
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
n=10: sigma[1,10]=18, sigma[1,10]=130 Intersection[{1,2,3,6,9,18},{1,2,5,10,13,26,65,130}]={1,2}, so a(10)=2.
|
|
MATHEMATICA
|
g1[x_] := Divisors[DivisorSigma[1, x]] g2[x_] := Divisors[DivisorSigma[2, x]] ncd[x_] := Length[Intersection[g1[x], g2[x]]] Table[ncd[w], {w, 1, 128}]
(* Second program: *)
Table[Length@ Apply[Intersection, Divisors@ Array[DivisorSigma[#, n] &, 2]], {n, 105}] (* Michael De Vlieger, Nov 23 2017 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|