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A260256 Numbers n such that tau(n + 2) = tau(n - 2) where tau(k) = A000005(k).

%I A260256 #13 Sep 08 2022 08:46:13
%S A260256 5,8,9,12,15,21,24,30,36,37,39,45,53,60,67,68,69,81,84,89,93,99,105,
%T A260256 111,112,113,117,120,121,127,129,131,143,144,157,158,165,172,173,184,
%U A260256 185,188,195,202,203,204,207,211,215,216,217,219,222,225,226,231,248,251,276,277,279,284,288
%N A260256 Numbers n such that tau(n + 2) = tau(n - 2) where tau(k) = A000005(k).
%C A260256 Pinner proves that this sequence is infinite, and in particular a(n) << n (log n)^7. The correct order is conjectured to be around n sqrt(log n). - _Charles R Greathouse IV_, Jul 21 2015
%H A260256 Charles R Greathouse IV, <a href="/A260256/b260256.txt">Table of n, a(n) for n = 1..10000</a>
%H A260256 Christopher G. Pinner, <a href="http://qjmath.oxfordjournals.org/content/48/4/499.extract">Repeated values of the divisor function</a>, Quart. J. Math. Oxford Ser. (2) 48:192 (1997), pp. 499-502.
%F A260256 A000005(a(n) + 2) = A000005(a(n) - 2).
%e A260256 8 is a member as 10 and 6 both have 4 divisors.
%t A260256 Select[ Range@ 290, DivisorSigma[0, # - 2] == DivisorSigma[0, # + 2] &] (* _Robert G. Wilson v_, Jul 21 2015 *)
%o A260256 (Magma)  [ n : n in [3..300] | Denominator((NumberOfDivisors(n-2))/(NumberOfDivisors(n+2))) eq 1 and Denominator((NumberOfDivisors(n+2))/(NumberOfDivisors(n-2))) eq 1];
%o A260256 (PARI) is(n)=n>4&&numdiv(n-2)==numdiv(n+2) \\ _Charles R Greathouse IV_, Jul 21 2015
%Y A260256 Cf. A067888, A067889.
%K A260256 nonn
%O A260256 1,1
%A A260256 _Juri-Stepan Gerasimov_, Jul 21 2015