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A195685
Primes p for which tau(2p-1) = tau(2p+1) = 4.
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
KEYWORD
nonn
AUTHOR
Timothy L. Tiffin, Sep 22 2011
STATUS
approved