A353040 - OEIS

%I #8 Apr 19 2022 07:26:17

%S 1,6,60,420,5460,791700,93284100,3915147600,285805774800

%N Unitary harmonic numbers (A006086) with a record number of unitary divisors.

%C The corresponding record values are 1, 4, 8, 16, 32, 64, 128, 256, 512, ...

%e The first 6 unitary harmonic numbers are 1, 6, 45, 60, 90, and 420. Their numbers of unitary divisors (A034444) are 1, 4, 4, 8, 8 and 16. The record values, 1, 4, 8 and 16 occur at 1, 6, 60 and 420, the first 4 terms of this sequence.

%t f[p_, e_] := 2 * p^e/(p^e + 1); r[n_] := Times @@ f @@@ FactorInteger[n]; dm = 0; s = {}; Do[h = r[n]; If[IntegerQ[h] && (d = 2^PrimeNu[n]) > dm, dm = d; AppendTo[s, n]], {n, 1, 10^6}]; s

%Y Cf. A006086, A034444, A335317.

%K nonn,more

%O 1,2

%A _Amiram Eldar_, Apr 19 2022