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A348200
Terms of A348004 having more unitary divisors than any smaller term.
0
1, 3, 12, 60, 660, 9240, 157080, 2984520, 68643960, 3226266120
OFFSET
1,2
COMMENTS
The corresponding numbers of unitary divisors are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ... (apparently, all the powers of 2).
a(11) > 7*10^10, if it exists.
EXAMPLE
The sequence A348004 begins with 1, 3, 4, 5, 7, 8, 9, 11 and 12. The number of unitary divisors of these terms are 1, 2, 2, 2, 2, 2, 2, 2 and 4, respectively. The record values, 1, 2 and 4, occur at 1, 3 and 12, the first 3 terms of this sequence.
MATHEMATICA
f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; q[n_] := Length @ Union[uphi /@ (d = Select[Divisors[n], CoprimeQ[#, n/#] &])] == Length[d]; dm = 0; s = {}; Do[If[q[n], d = 2^PrimeNu[n]; If[d > dm, dm = d; AppendTo[s, n]]], {n, 1, 10^6}]; s
CROSSREFS
The unitary version of A348198.
Sequence in context: A211774 A002497 A228251 * A218092 A192479 A161799
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Oct 06 2021
STATUS
approved