A348657 Numbers k such that k and k+1 have the same denominator of the harmonic means of their unitary divisors.

266, 321, 1015, 2544, 4004, 4277, 5016, 15861, 28461, 47613, 63546, 135078, 137333, 203709, 207024, 265489, 344217, 383466, 517610, 603687, 787156, 798625, 876469, 1100835, 1713865, 2062863, 2246923, 2349390, 2666741, 3013830, 3961129, 5048409, 6148960, 6491717

Offset: 1

Author

Amiram Eldar, Oct 28 2021

Keywords

• nonn

Comments

Numbers k such that A103340(k) = A103340(k+1).

The common denominators of k and k+1 are 30, 36, 36, 153, 15, 96, 45, 936, ...

Can 3 consecutive numbers have the same denominator of harmonic mean of unitary divisors? There are no such numbers below 2.5*10^10.

Examples

			266 is a term since the harmonic means of the unitary divisors of 266 and 267 are 133/30 and 89/30, respectively, and both have the denominator 30.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..400

Crossrefs

The unitary version of A348415.

Cf. A103339, A103340.

Programs

Mathematica

f[p_, e_] := 2/(1 + p^(-e)); d[n_] := Denominator[Times @@ f @@@ FactorInteger[n]]; Select[Range[10^5], d[#] == d[# + 1] &]