A195685 Primes p for which tau(2p-1) = tau(2p+1) = 4.

17, 43, 47, 71, 101, 107, 109, 151, 197, 223, 317, 349, 461, 521, 569, 631, 673, 701, 821, 881, 919, 947, 971, 991, 1051, 1091, 1109, 1153, 1181, 1217, 1231, 1259, 1321, 1361, 1367, 1549, 1693, 1801, 1847, 1933, 1951, 1979, 2143, 2207, 2267, 2297, 2441, 2801

Offset

1,1

Comments

Sequence terms are a subset of those listed in A086006 and A068497.

The numbers 2p-1, 2p, 2p+1 form a run (indeed, a maximal run) of three consecutive integers each with four positive divisors. The first two examples are 33, 34, 35 and 85, 86, 87. A039833 gives the first number in these maximal 3-integer runs. - Timothy L. Tiffin, Jul 05 2016

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = A248201(n)/2. - Torlach Rush, Jun 25 2021

Example

tau(2*17-1) = tau(33) = tau(3*11) = 4 = tau(5*7) = tau(35) = tau(2*17+1) and tau(2*43-1) = tau(85) = tau(5*17) = 4 = tau(3*29) = tau(87) = tau(2*43+1). - Timothy L. Tiffin, Jul 05 2016

Maple

with(numtheory):
q:= p-> isprime(p) and tau(2*p-1)=4 and tau(2*p+1)=4:
select(q, [$1..3000])[];  # Alois P. Heinz, Apr 18 2019

Mathematica

Select[Prime[Range[500]], DivisorSigma[0, 2 # - 1] == DivisorSigma[0, 2 # + 1] == 4 &] (* T. D. Noe, Sep 22 2011 *)
Select[Mean[#]/2&/@SequencePosition[DivisorSigma[0, Range[6000]], {4, _, 4}], PrimeQ] (* Harvey P. Dale, Nov 26 2021 *)

Prog

(PARI) lista(nn) = forprime(p=2, nn, if ((numdiv(2*p-1) == 4) && (numdiv(2*p+1) == 4), print1(p, ", "))); \\ Michel Marcus, Jul 06 2016

Crossrefs

Cf. A039833, A068497, A086006, A248201.

Sequence in context: A196209 A196476 A086006 * A118587 A215164 A123592

Adjacent sequences: A195682 A195683 A195684 * A195686 A195687 A195688

Keyword

nonn

Author

Timothy L. Tiffin, Sep 22 2011

Status

approved