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%I #9 Sep 20 2016 09:48:32
%S 1,3,14,35,42,70,105,119,209,210,238,248,297,357,412,418,477,594,595,
%T 616,627,714,744,954,1045,1142,1178,1190,1236,1240,1254,1328,1339,
%U 1463,1485,1672,1674,1703,1736,1785,1848,1863,2079,2090,2376,2385,2540,2728
%N Numbers n such that sum of the distinct prime factors of phi(n) = sum of the distinct prime factors of sigma(n).
%H Charles R Greathouse IV, <a href="/A076533/b076533.txt">Table of n, a(n) for n = 1..10000</a>
%e sopf(sigma(14)) = 5; sopf(phi(14))) = 5; hence 14 is a term of the sequence.
%t p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[3, 10^4], p[DivisorSigma[1, # ]] == p[EulerPhi[ # ]] &]
%t Select[Range[3000],Total[FactorInteger[DivisorSigma[1,#]][[All,1]]] == Total[ FactorInteger[EulerPhi[#]][[All,1]]]&] (* _Harvey P. Dale_, Sep 20 2016 *)
%o (PARI) sopf(n)=my(f=factor(n)[,1]); sum(i=1,#f,f[i])
%o is(n)=sopf(sigma(n))==sopf(eulerphi(n)) \\ _Charles R Greathouse IV_, Mar 09 2014
%Y Cf. A008472, A075565, A075784, A075846, A076525, A076527, A076531, A076532.
%K nonn
%O 1,2
%A _Joseph L. Pe_, Oct 18 2002
%E Edited by _Ray Chandler_, Feb 13 2005
%E a(1) inserted by _Charles R Greathouse IV_, Mar 09 2014
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