A081383 Least x = a(n) such that number of common prime factors (ignoring multiplicity) of sigma(x) = A000203(x) and phi(x) = A000010(x) equals n.

3, 14, 209, 3596, 41624, 2003639, 24206049, 2562857198, 57721363052

Offset: 1

Author

Labos Elemer, Mar 28 2003

Keywords

• nonn
• more

Comments

a(10) <= 6804704928496. - Donovan Johnson, Jun 15 2013

Examples

			x = 209: sigma(209) = 240 = 2^4*3*5, phi(209) = 180 = 2^2*3^2*5, common factor set = {2,3,5}, so a(3) = 209.
		

Crossrefs

Cf. A000203, A000010, A081396.

Programs

Mathematica

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] t=Table[0, {10}]; Do[s=Length[Intersection[ba[EulerPhi[n]], ba[DivisorSigma[1, n]]]]; If[s<11&&t[[s]]==0, t[[s]]=n], {n, 1, 1000000}]; t

PARI

a(n)=my(k=prod(i=1,n,prime(i))); while(omega(gcd(sigma(k),eulerphi(k)))!=n, k++); k \\ Charles R Greathouse IV, Feb 14 2013

Formula

a(n) = min{x: A081396(x) = n}.

Extensions

a(6)-a(8) from Donovan Johnson, May 24 2009

a(9) from Donovan Johnson, Jun 14 2013