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

Author

Timothy L. Tiffin, Sep 22 2011

Keywords

• nonn

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

Examples

			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
		

Links

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

Crossrefs

Cf. A039833, A068497, A086006, A248201.

Programs

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 *)

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

Formula

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