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

5, 8, 9, 12, 15, 21, 24, 30, 36, 37, 39, 45, 53, 60, 67, 68, 69, 81, 84, 89, 93, 99, 105, 111, 112, 113, 117, 120, 121, 127, 129, 131, 143, 144, 157, 158, 165, 172, 173, 184, 185, 188, 195, 202, 203, 204, 207, 211, 215, 216, 217, 219, 222, 225, 226, 231, 248, 251, 276, 277, 279, 284, 288

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 21 2015

Keywords

• nonn

Comments

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

Examples

			8 is a member as 10 and 6 both have 4 divisors.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Christopher G. Pinner, Repeated values of the divisor function, Quart. J. Math. Oxford Ser. (2) 48:192 (1997), pp. 499-502.

Crossrefs

Cf. A067888, A067889.

Programs

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];

Mathematica

Select[ Range@ 290, DivisorSigma[0, # - 2] == DivisorSigma[0, # + 2] &] (* Robert G. Wilson v, Jul 21 2015 *)

PARI

is(n)=n>4&&numdiv(n-2)==numdiv(n+2) \\ Charles R Greathouse IV, Jul 21 2015

Formula

A000005(a(n) + 2) = A000005(a(n) - 2).