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

1,1

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.

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A099377, A099378.

Similar sequences: A002961, A238380.

Sequence in context: A137207 A206765 A228500 * A082814 A178257 A057406

Adjacent sequences: A348412 A348413 A348414 * A348416 A348417 A348418

Keyword

nonn

Author

Amiram Eldar, Oct 17 2021

Status

approved