A348200 Terms of A348004 having more unitary divisors than any smaller term.

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.

Links

Table of n, a(n) for n=1..10.

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.

Cf. A348002, A348004.

Sequence in context: A211774 A002497 A228251 * A218092 A192479 A161799

Adjacent sequences: A348197 A348198 A348199 * A348201 A348202 A348203

Keyword

nonn,more

Author

Amiram Eldar, Oct 06 2021

Status

approved