|
|
A270414
|
|
Numbers n such that sigma(n-1) and sigma(phi(n)) are both primes.
|
|
2
|
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
There are no other terms <= 10^7.
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.
|
|
LINKS
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|