A270415 -id:A270415 - cp's OEIS frontend

A249759 Primes p such that sigma(p-1) is a prime q.

3, 5, 17, 65537

Offset: 1

Jaroslav Krizek, Nov 13 2014

Subsequence of {A023194(n)+1}.
Conjectures: 1) sequence is finite; 2) sequence is a subsequence of A019434 (Fermat primes); 3) sequence consists of Fermat primes p such that sigma(p-1) is a Mersenne prime; 4) a(n) = (A249761(n)+3)/2.
3 is the only prime p such that sigma(p+1) is prime, i.e., 3 is the only prime p such that sigma(p-1) and sigma(p+1) are both primes.
Conjecture: 3 is the only number n such that n and sigma(n+1) are both prime.
Primes p such that A051027(p-1) = sigma(sigma(p-1)) = 2*(p-1). Subsequence of A256438. - Jaroslav Krizek, Mar 29 2015
From Jaroslav Krizek, Mar 17 2016: (Start)
Primes p such that A000203(A000010(p)) = sigma(phi(p)) is a prime.
Prime terms from A062514 and A270413, A270414, A270415 and A270416. (End)
From Jaroslav Krizek, Nov 27 2016: (Start)
Corresponding values of primes q are in A249761: 3, 7, 31, 131071, ...
Conjecture: subsequence of A256438 and A278741.
Conjecture: also primes p such that tau(p-1) is a prime q; corresponding values of primes q are 2, 3, 5, 17. (End)

			Prime 17 is in the sequence because sigma(17-1) = sigma(16) = 31 (prime).

Cf. A000203, A000668, A019434, A023194, A249760, A249761.

[p: p in PrimesUpTo(1000000) | IsPrime(SumOfDivisors(p-1))]

with(numtheory): A249759:=n->`if`(isprime(n) and isprime(sigma(n-1)), n, NULL): seq(A249759(n), n=1..6*10^5); # Wesley Ivan Hurt, Nov 14 2014

Select[Range[10^5], PrimeQ[#]&& PrimeQ[DivisorSigma[1, # - 1]] &] (* Vincenzo Librandi, Nov 14 2014 *)
Select[Prime[Range[7000]],PrimeQ[DivisorSigma[1,#-1]]&] (* Harvey P. Dale, Jun 14 2020 *)

lista(nn) = {forprime(p=1, nn, if (isprime(sigma(p-1)), print1(p, ", ")););} \\ Michel Marcus, Nov 14 2014

a(n) = A249760(n) + 1.

Sigma(a(n)-1) = A249761(n).

A270413 Numbers m such that sigma(m-1) is a prime.

Original entry on oeis.org

3, 5, 10, 17, 26, 65, 290, 730, 1682, 2402, 3482, 4097, 5042, 7922, 10202, 15626, 17162, 27890, 28562, 29930, 65537, 83522, 85850, 146690, 262145, 279842, 458330, 491402, 531442, 552050, 579122, 597530, 683930, 703922, 707282, 734450, 829922, 1190282, 1203410

Offset: 1

Jaroslav Krizek, Mar 16 2016

nonn

Prime terms are in A249759.
Corresponding values of sigma(n-1): 3, 7, 13, 31, 31, 127, 307, 1093, ...
Conjecture: supersequence of A256438.
Conjecture: 31 is the only prime p such that p = sigma(x-1) = sigma(y-1) for distinct numbers x and y; 31 = sigma(17-1) = sigma(26-1).
Supersequence of A270414 and A270415.

			17 is in the sequence because sigma(17-1) = sigma(16) = 31 (prime).

Cf. A000203, A023194, A249759, A256438, A270414, A270415.

[n: n in [2..2000000] |  IsPrime(SumOfDivisors(n-1))];

Select[Range[10^6], PrimeQ@ DivisorSigma[1, # - 1] &] (* Michael De Vlieger, Mar 17 2016 *)

isok(n) = isprime(sigma(n-1)); \\ Michel Marcus, Mar 17 2016

a(n) = A023194(n) + 1.

cp's OEIS Frontend

A249759 Primes p such that sigma(p-1) is a prime q.

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