A353692 - OEIS

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.

%I #11 May 05 2022 08:59:10

%S 6,20,45,72,30,60,42,272,756,120,66,18,78,140,1890,720,102,180,114,24,

%T 315,220,138,360,150,260,3321,504,174,7560,186,1440,495,340,210,52416,

%U 222,380,585,1360,246,420,258,792,1512,460,282,720,294,600,765,936,318

%N 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.

%H Amiram Eldar, <a href="/A353692/b353692.txt">Table of n, a(n) for n = 1..399</a>

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

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

%t 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]

%Y Cf. A103339, A103340.

%Y Similar sequences: A069789, A069797, A069805, A353691.

%K nonn

%O 1,1

%A _Amiram Eldar_, May 04 2022