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A284202
Numbers m such that phi(sum of divisors of m) = lambda(sum of distinct primes dividing m).
0
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
1,1
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.
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Mar 22 2017
STATUS
approved