A076533 Numbers n such that sum of the distinct prime factors of phi(n) = sum of the distinct prime factors of sigma(n).

1, 3, 14, 35, 42, 70, 105, 119, 209, 210, 238, 248, 297, 357, 412, 418, 477, 594, 595, 616, 627, 714, 744, 954, 1045, 1142, 1178, 1190, 1236, 1240, 1254, 1328, 1339, 1463, 1485, 1672, 1674, 1703, 1736, 1785, 1848, 1863, 2079, 2090, 2376, 2385, 2540, 2728

Offset: 1

Author

Joseph L. Pe, Oct 18 2002

Keywords

• nonn

Examples

			sopf(sigma(14)) = 5; sopf(phi(14)) = 5; hence 14 is a term of the sequence.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008472, A075565, A075784, A075846, A076525, A076527, A076531, A076532.

Programs

Mathematica

p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[3, 10^4], p[DivisorSigma[1, # ]] == p[EulerPhi[ # ]] &]
Select[Range[3000],Total[FactorInteger[DivisorSigma[1,#]][[All,1]]] == Total[ FactorInteger[EulerPhi[#]][[All,1]]]&] (* Harvey P. Dale, Sep 20 2016 *)

PARI

sopf(n)=my(f=factor(n)[,1]); sum(i=1,#f,f[i])
is(n)=sopf(sigma(n))==sopf(eulerphi(n)) \\ Charles R Greathouse IV, Mar 09 2014

Extensions

Edited by Ray Chandler, Feb 13 2005

a(1) inserted by Charles R Greathouse IV, Mar 09 2014