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A270414
Numbers n such that sigma(n-1) and sigma(phi(n)) are both primes.
2
3, 5, 10, 17, 65537
OFFSET
1,1
COMMENTS
Numbers n such that A000203(n-1) and A062402(n) are both primes.
There are no other terms <= 10^7.
Intersection of A270413 and A062514.
Prime terms are in A249759.
Corresponding values of sigma(n-1): 3, 7, 13, 31, 131071, ...
Corresponding values of sigma(phi(n)): 3, 7, 7, 31, 131071, ...
Conjecture: union of number 10 and A249759.
EXAMPLE
10 is in the sequence because sigma(10-1) = sigma(9) = 13 and sigma(phi(10)) = sigma(4) = 7 (both primes).
MATHEMATICA
Select[Range[10^6], And[PrimeQ@ DivisorSigma[1, # - 1], PrimeQ@ DivisorSigma[1, EulerPhi@ #]] &] (* Michael De Vlieger, Mar 17 2016 *)
PROG
(Magma) [n: n in [2..100000] | IsPrime(SumOfDivisors(n-1)) and IsPrime(SumOfDivisors(EulerPhi(n)))]
(PARI) isok(n) = isprime(sigma(n-1)) && isprime(sigma(eulerphi(n))); \\ Michel Marcus, Mar 17 2016
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jaroslav Krizek, Mar 16 2016
STATUS
approved