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%I #21 Apr 05 2020 13:26:25
%S 40,50,54,171,195,231,330,377,387,518,638,742,745,888,1057,1141,1397,
%T 1561,1788,2422,2682,2763,3206,3357,3805,4037,4344,4382,4915,5093,
%U 5138,5391,5558,5951,6147,8063,8952,9132,9422,10109,10968,11796,12287,12481
%N Numbers k>1 such that phi(phi(k))= sigma(sopf(k)).
%C sopf(k) is the sum of the distinct primes dividing k (without repetition): A008472), phi(k) is the Euler totient function (A000010), sigma(k) is the sum of divisors of k (A000203).
%H Amiram Eldar, <a href="/A173337/b173337.txt">Table of n, a(n) for n = 1..1000</a>
%F k such that A010554(k)= sigma(A008472(k)).
%e 40 is in the sequence because phi(40)= 16, phi(16) = 8, sopf(40) = 7 and sigma(7) = 8;
%e 171 is in the sequence because phi(171) = 108, phi(108) = 36, sopf(171) = 22 and sigma(22) = 36.
%p with(numtheory) :
%p A008472 := proc(n)
%p add(p, p = factorset(n):
%p end proc:
%p isA173337 := proc(n)
%p phi(phi(n)) = sigma(A008472(n)) ;
%p end proc:
%p for n from 1 do
%p if isA173337(n) then printf("%d,",n) ; fi;
%p end do: # _R. J. Mathar_, Jul 06 2012
%t sopf[n_] := Plus @@ (First@# & /@ FactorInteger[n]); Select[Range[2, 13000], EulerPhi[EulerPhi[#]] == DivisorSigma[1, sopf[#]] &] (* _Amiram Eldar_, Jul 09 2019 *)
%t Select[Range[2,15000],DivisorSigma[1,Total[FactorInteger[#][[All,1]]]] == EulerPhi[ EulerPhi[#]]&] (* _Harvey P. Dale_, Apr 05 2020 *)
%o (PARI) isok(n) = (n>1) && eulerphi(eulerphi(n)) == sigma(vecsum(factor(n)[, 1])); \\ _Michel Marcus_, Jul 10 2019
%Y Cf. A000010, A000203, A010554, A008472.
%K nonn
%O 1,1
%A _Michel Lagneau_, Feb 16 2010
%E Definition clarified by _N. J. A. Sloane_, Apr 05 2020
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