A284202 - OEIS

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

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OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..25.

EXAMPLE

34 is in the sequence because A000010(A000203(34)) = A000010(54) = 18, and

A002322(A008472(34)) = A002322(19) = 18.

MATHEMATICA

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

PROG

(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

CROSSREFS

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

Sequence in context: A372851 A362909 A282515 * A275189 A091616 A117224

Adjacent sequences: A284199 A284200 A284201 * A284203 A284204 A284205

KEYWORD

nonn

AUTHOR

Michel Lagneau, Mar 22 2017

STATUS

approved