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A353040
Unitary harmonic numbers (A006086) with a record number of unitary divisors.
0
1, 6, 60, 420, 5460, 791700, 93284100, 3915147600, 285805774800
OFFSET
1,2
COMMENTS
The corresponding record values are 1, 4, 8, 16, 32, 64, 128, 256, 512, ...
EXAMPLE
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.
MATHEMATICA
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
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Apr 19 2022
STATUS
approved