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

Author

Michel Lagneau, Mar 22 2017

Keywords

• nonn
• more

Comments

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.

Examples

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

Crossrefs

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

Programs

Mathematica

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

PARI

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