login
A081396
Number of common prime factors (ignoring multiplicity) of sigma(n) = A000203(n) and phi(n) = A000010(n).
5
0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 0, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 0, 1, 1, 1, 2, 2
OFFSET
1,14
LINKS
FORMULA
a(n) = A001221(A009223(n)). - Antti Karttunen, Jan 22 2020
EXAMPLE
n=209: sigma(209) = 240 = 2*2*2*2*3*5, phi(209) = 180 = 2*2*3*3*5, common factor set = {2,3,5}, so a(209)=3.
MATHEMATICA
ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] Table[Length[Intersection[ba[EulerPhi[w]], ba[DivisorSigma[1, w]]]], {w, 1, 100}]
PROG
(PARI) a(n)=omega(gcd(sigma(n), eulerphi(n))) \\ Charles R Greathouse IV, Feb 19 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Mar 28 2003
EXTENSIONS
Data section extended up to a(105) by Antti Karttunen, Jan 22 2020
STATUS
approved