A353692 a(n) is the least number k > n such that uh(k)/uh(n) is an integer, where uh(n) is the harmonic mean of the unitary divisors of n, or -1 if no such k exists.

6, 20, 45, 72, 30, 60, 42, 272, 756, 120, 66, 18, 78, 140, 1890, 720, 102, 180, 114, 24, 315, 220, 138, 360, 150, 260, 3321, 504, 174, 7560, 186, 1440, 495, 340, 210, 52416, 222, 380, 585, 1360, 246, 420, 258, 792, 1512, 460, 282, 720, 294, 600, 765, 936, 318

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..399

Formula

a(p) = 6*p for a prime p > 3.

Example

a(2) = 20 since 20 is the least number > 2 such that uh(20)/uh(2) = (8/3)/(4/3) = 2 is an integer.

Mathematica

uh[n_] := Module[{f = FactorInteger[n]}, n*2^Length[f]/Times @@ (1 + Power @@@ f)]; a[n_] := Module[{k = n + 1, uhn = uh[n]}, While[!IntegerQ[uh[k]/uhn], k++]; k]; Array[a, 30]

Crossrefs

Cf. A103339, A103340.

Similar sequences: A069789, A069797, A069805, A353691.

Sequence in context: A006137 A225269 A048969 * A005564 A011928 A055455

Adjacent sequences: A353689 A353690 A353691 * A353693 A353694 A353695

Keyword

nonn

Author

Amiram Eldar, May 04 2022

Status

approved