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 A292448 Primes q of the form sigma((p + 1) / 2) where p is a prime. 2
 3, 7, 13, 31, 127, 307, 1723, 2801, 3541, 8191, 19531, 86143, 131071, 492103, 524287, 552793, 684757, 704761, 735307, 797161, 1353733, 1886503, 3413257, 3894703, 5473261, 7094233, 7781311, 9250723, 10378063, 12655807, 18143341, 19443691, 22292563, 23907211 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 = p. 2801 is the smallest term of the form 6*k + 5. The next one is 39449441. Note that both of them are of the form 1 + t + t^2 + t^3 + t^4 where t is a prime number. - Altug Alkan, Oct 03 2017 LINKS Table of n, a(n) for n=1..34. EXAMPLE Prime 13 is a term because there is prime 17 with sigma((17 + 1) / 2) = sigma(9) = 13. MATHEMATICA max = 10^6; Select[Union@ Reap[Do[If[PrimeQ@ #, Sow@ #] &@DivisorSigma[1, (Prime@ i + 1)/2], {i, max}] ][[-1, 1]], # < Prime[max]/2 &] (* Michael De Vlieger, Sep 16 2017, corrected by Amiram Eldar, Oct 08 2021 *) PROG (Magma) m := 5*10^7; Set(Sort([SumOfDivisors((n+1) div 2): n in [1..2*m] | IsPrime(n) and IsPrime(SumOfDivisors((n+1) div 2)) and SumOfDivisors((n+1) div 2) le m])) // corrected by Amiram Eldar, Oct 08 2021 (PARI) lista(nn) = {my(list = List()); forprime(p=3, 2*nn, if (isprime(q=sigma((p+1)/2)), listput(list, q)); ); select(x->(x <= nn), vecsort(Vec(list))); } \\ Michel Marcus, Oct 08 2021 CROSSREFS Cf. A000203, A000668, A292447. Sequence in context: A087578 A023195 A100382 * A222227 A152981 A112040 Adjacent sequences: A292445 A292446 A292447 * A292449 A292450 A292451 KEYWORD nonn AUTHOR Jaroslav Krizek, Sep 16 2017 STATUS approved

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Last modified August 6 06:50 EDT 2024. Contains 374960 sequences. (Running on oeis4.)