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%I #36 Nov 26 2021 14:48:05
%S 17,43,47,71,101,107,109,151,197,223,317,349,461,521,569,631,673,701,
%T 821,881,919,947,971,991,1051,1091,1109,1153,1181,1217,1231,1259,1321,
%U 1361,1367,1549,1693,1801,1847,1933,1951,1979,2143,2207,2267,2297,2441,2801
%N Primes p for which tau(2p-1) = tau(2p+1) = 4.
%C Sequence terms are a subset of those listed in A086006 and A068497.
%C 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
%H Charles R Greathouse IV, <a href="/A195685/b195685.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A248201(n)/2. - _Torlach Rush_, Jun 25 2021
%e 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
%p with(numtheory):
%p q:= p-> isprime(p) and tau(2*p-1)=4 and tau(2*p+1)=4:
%p select(q, [$1..3000])[]; # _Alois P. Heinz_, Apr 18 2019
%t Select[Prime[Range[500]], DivisorSigma[0, 2 # - 1] == DivisorSigma[0, 2 # + 1] == 4 &] (* _T. D. Noe_, Sep 22 2011 *)
%t Select[Mean[#]/2&/@SequencePosition[DivisorSigma[0,Range[6000]],{4,_,4}],PrimeQ] (* _Harvey P. Dale_, Nov 26 2021 *)
%o (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
%Y Cf. A039833, A068497, A086006, A248201.
%K nonn
%O 1,1
%A _Timothy L. Tiffin_, Sep 22 2011
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