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

1,1

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.

Links

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

Example

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.

Mathematica

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

Crossrefs

The unitary version of A348415.

Cf. A103339, A103340.

Sequence in context: A278141 A091676 A061662 * A321224 A028528 A260134

Adjacent sequences: A348654 A348655 A348656 * A348658 A348659 A348660

Keyword

nonn

Author

Amiram Eldar, Oct 28 2021

Status

approved