A292446 Numbers k such that sigma((k + 1) / 2) is a prime q.

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

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

Cf. A000203, A000668, A023194, A023195, A062700, A292447, A292448.

Sequence in context: A123988 A006628 A068682 * A045425 A364189 A099983

Adjacent sequences: A292443 A292444 A292445 * A292447 A292448 A292449

Keyword

nonn,easy

Author

Jaroslav Krizek, Sep 16 2017

Status

approved