A348415 Numbers k such that k and k+1 have the same denominator of the harmonic means of their divisors.

12, 88, 180, 266, 321, 604, 4277, 4364, 8632, 15861, 18720, 28461, 47613, 63546, 97412, 98907, 135078, 137333, 154132, 179621, 185776, 192699, 203709, 265489, 284883, 344217, 383466, 517610, 604197, 876469, 1089604, 1277518, 1713865, 1839123, 1893268, 2349390

Offset: 1

Author

Amiram Eldar, Oct 17 2021

Keywords

• nonn

Comments

Numbers k such that A099378(k) = A099378(k+1).

The common denominators of k and k+1 are 7, 45, 91, 30, 36, 133, 96, 637, ...

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

Examples

			12 is a term since the harmonic means of the divisors of 12 and 13 are 18/7 and 13/7, respectively, and both have the denominator 7.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A099377, A099378.

Similar sequences: A002961, A238380.

Programs

Mathematica

dh[n_] := Denominator[DivisorSigma[0, n]/DivisorSigma[-1, n]]; Select[Range[10^6], dh[#] == dh[# + 1] &]

PARI

f(n) = my(d=divisors(n)); denominator(#d/sum(k=1, #d, 1/d[k])); \\ A099378
isok(k) = f(k) == f(k+1); \\ Michel Marcus, Oct 20 2021