A282515 -id:A282515 - cp's OEIS frontend

A284202 Numbers m such that phi(sum of divisors of m) = lambda(sum of distinct primes dividing m).

3, 6, 10, 22, 34, 142, 214, 382, 862, 2302, 5182, 279934, 944782, 1572862, 1990654, 114791254, 127401982, 339738622, 8153726974, 21743271934, 4696546738174, 112717121716222, 158329674399742, 169075682574334, 300578991243262

Offset: 1

Michel Lagneau, Mar 22 2017

Or numbers m such that A000010(A000203(m)) = A002322(A008472(m)), where phi is the Euler totient function and lambda is Carmichael's function.
Properties of the sequence:
(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).
(2) {a(n)} is included in {A282515(n)}.
(3) for n > 2, a(n)/2 is a prime number congruent to 5 mod 6.

			34 is in the sequence because A000010(A000203(34)) = A000010(54) = 18, and
A002322(A008472(34)) = A002322(19) = 18.

Cf. A000010, A000203, A002322, A008472, A078883, A282515.

Select[Range[10^6], EulerPhi@ DivisorSigma[1, #] == CarmichaelLambda[Total@ FactorInteger[#][[All, 1]]] &]

lambda(n) = lcm(znstar(n)[2]); \\ after Charles R Greathouse IV in A002322
sopf(n) = vecsum(factor(n)[,1])
isok(n) = eulerphi(sigma(n)) == lambda(sopf(n)) \\ Indranil Ghosh, Mar 22 2017

cp's OEIS Frontend

A284202 Numbers m such that phi(sum of divisors of m) = lambda(sum of distinct primes dividing m).

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