A292448 -id:A292448 - cp's OEIS frontend

A292447 Primes p such that sigma((p + 1) / 2) is a prime q.

3, 7, 17, 31, 127, 577, 3361, 4801, 6961, 8191, 31249, 131071, 171697, 524287, 982801, 1062881, 1104097, 1367857, 1407841, 1468897, 2705137, 3770257, 6822817, 7785457, 10941841, 14183137, 15557041, 18495361, 20749681, 25304497, 36278161, 38878561, 44575681

Offset: 1

Jaroslav Krizek, Sep 16 2017

A companion sequence of A249902.
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.
A subsequence of A178490. - Altug Alkan, Oct 02 2017

			17 is a term because sigma((17 + 1) / 2) = sigma(9) = 13 (prime).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000203, A000668, A178490, A249902, A292448.

[n: n in [1..10^8] | IsPrime(n) and IsPrime(SumOfDivisors((n+1) div 2))];

Select[Prime@ Range[10^6], PrimeQ@ DivisorSigma[1, (# + 1)/2] &] (* Michael De Vlieger, Sep 16 2017 *)

lista(nn) = forprime(p=3, nn, if(isprime(sigma((p+1)/2)), print1(p, ", "))); \\ Altug Alkan, Oct 02 2017

a(n) = 2*A249902(n) - 1. - Altug Alkan, Oct 02 2017

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

Original entry on oeis.org

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

Jaroslav Krizek, Sep 16 2017

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

			49 is a term because sigma((49 + 1) / 2) = sigma(25) = 31 (prime).

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

[n: n in [1..10^8] | IsOdd(n) and IsPrime(SumOfDivisors((n+1) div 2))];

Select[Range[1,166*10^4,2],PrimeQ[DivisorSigma[1,(#+1)/2]]&] (* Harvey P. Dale, Jun 22 2022 *)

isok(n) = (n%2) && isprime(sigma((n+1)/2)); \\ Michel Marcus, Sep 16 2017

a(n) = 2*A023194(n) - 1.

cp's OEIS Frontend

A292447 Primes p such that sigma((p + 1) / 2) is a prime q.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula