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A292446
Numbers k such that sigma((k + 1) / 2) is a prime q.
1
3, 7, 17, 31, 49, 127, 577, 1457, 3361, 4801, 6961, 8191, 10081, 15841, 20401, 31249, 34321, 55777, 57121, 59857, 131071, 167041, 171697, 293377, 524287, 559681, 916657, 982801, 1062881, 1104097, 1158241, 1195057, 1367857, 1407841, 1414561, 1468897, 1659841
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
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
KEYWORD
nonn,easy
AUTHOR
Jaroslav Krizek, Sep 16 2017
STATUS
approved