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A173337 Numbers k>1 such that phi(phi(k)) = sigma(sopf(k)).

%I A173337 #27 Feb 08 2025 01:23:30
%S A173337 40,50,54,171,195,231,330,377,387,518,638,742,745,888,1057,1141,1397,
%T A173337 1561,1788,2422,2682,2763,3206,3357,3805,4037,4344,4382,4915,5093,
%U A173337 5138,5391,5558,5951,6147,8063,8952,9132,9422,10109,10968,11796,12287,12481
%N A173337 Numbers k>1 such that phi(phi(k)) = sigma(sopf(k)).
%H A173337 Amiram Eldar, <a href="/A173337/b173337.txt">Table of n, a(n) for n = 1..1000</a>
%F A173337 k such that A010554(k) = A000203(A008472(k)).
%e A173337 40 is in the sequence because phi(40)= 16, phi(16) = 8, sopf(40) = 7 and sigma(7) = 8;
%e A173337 171 is in the sequence because phi(171) = 108, phi(108) = 36, sopf(171) = 22 and sigma(22) = 36.
%p A173337 with(numtheory) :
%p A173337 A008472 := proc(n)
%p A173337         add(p, p = factorset(n):
%p A173337 end proc:
%p A173337 isA173337 := proc(n)
%p A173337         phi(phi(n)) = sigma(A008472(n)) ;
%p A173337 end proc:
%p A173337 for n from 1 do
%p A173337         if isA173337(n) then printf("%d,",n) ; fi;
%p A173337 end do: # _R. J. Mathar_, Jul 06 2012
%t A173337 sopf[n_] := Plus @@ (First@# & /@ FactorInteger[n]); Select[Range[2, 13000], EulerPhi[EulerPhi[#]] == DivisorSigma[1, sopf[#]] &] (* _Amiram Eldar_, Jul 09 2019 *)
%t A173337 Select[Range[2,15000],DivisorSigma[1,Total[FactorInteger[#][[All,1]]]] == EulerPhi[ EulerPhi[#]]&] (* _Harvey P. Dale_, Apr 05 2020 *)
%o A173337 (PARI) isok(n) = (n>1) && eulerphi(eulerphi(n)) == sigma(vecsum(factor(n)[, 1])); \\ _Michel Marcus_, Jul 10 2019
%Y A173337 Cf. A000010 (Euler totient function), A000203 (sum of divisors), A008472 (sum of prime factors), A010554.
%K A173337 nonn
%O A173337 1,1
%A A173337 _Michel Lagneau_, Feb 16 2010
%E A173337 Definition clarified by _N. J. A. Sloane_, Apr 05 2020