OFFSET
1,1
COMMENTS
Corresponding values of primes q are in A062700.
Prime terms are in A292447.
Mersenne primes p = 2^k - 1 (A000668) are terms: sigma((p + 1) / 2) = sigma((2^k - 1 + 1) / 2) = sigma((2^(k - 1)) = 2^k - 1.
This sequence also has terms of the form p^(q-1) where p and q are odd primes, i.e., A002315(1)^2 = 7^2 and A002315(3)^2 = 239^2. Terms that are not squarefree are 49, 55777, 57121, 167041, 2789521, 50060017, ... - Altug Alkan, Oct 02 2017
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = 2*A023194(n) - 1.
EXAMPLE
49 is a term because sigma((49 + 1) / 2) = sigma(25) = 31 (prime).
MATHEMATICA
Select[Range[1, 166*10^4, 2], PrimeQ[DivisorSigma[1, (#+1)/2]]&] (* Harvey P. Dale, Jun 22 2022 *)
PROG
(Magma) [n: n in [1..10^8] | IsOdd(n) and IsPrime(SumOfDivisors((n+1) div 2))]
(PARI) isok(n) = (n%2) && isprime(sigma((n+1)/2)); \\ Michel Marcus, Sep 16 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jaroslav Krizek, Sep 16 2017
STATUS
approved