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%I #18 Jan 13 2025 13:15:09
%S 3,6,10,22,34,142,214,382,862,2302,5182,279934,944782,1572862,1990654,
%T 114791254,127401982,339738622,8153726974,21743271934,4696546738174,
%U 112717121716222,158329674399742,169075682574334,300578991243262
%N Numbers m such that phi(sum of divisors of m) = lambda(sum of distinct primes dividing m).
%C Or numbers m such that A000010(A000203(m)) = A002322(A008472(m)), where phi is the Euler totient function and lambda is Carmichael's function.
%C Properties of the sequence:
%C (1) for n > 1, it seems that a(n) = 2*A078883(n) = 2*(Lesser member p of a twin prime pair such that p+1 is 3-smooth).
%C (2) {a(n)} is included in {A282515(n)}.
%C (3) for n > 2, a(n)/2 is a prime number congruent to 5 mod 6.
%e 34 is in the sequence because A000010(A000203(34)) = A000010(54) = 18, and
%e A002322(A008472(34)) = A002322(19) = 18.
%t Select[Range[10^6], EulerPhi@ DivisorSigma[1, #] == CarmichaelLambda[Total@ FactorInteger[#][[All, 1]]] &]
%o (PARI)
%o lambda(n) = lcm(znstar(n)[2]); \\ after _Charles R Greathouse IV_ in A002322
%o sopf(n) = vecsum(factor(n)[,1])
%o isok(n) = eulerphi(sigma(n)) == lambda(sopf(n)) \\ _Indranil Ghosh_, Mar 22 2017
%Y Cf. A000010, A000203, A002322, A008472, A078883, A282515.
%K nonn,more
%O 1,1
%A _Michel Lagneau_, Mar 22 2017