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

1, 3, 12, 60, 660, 9240, 157080, 2984520, 68643960, 3226266120

Offset: 1

Author

Amiram Eldar, Oct 06 2021

Keywords

• nonn
• more

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.

Examples

			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.
		

Crossrefs

The unitary version of A348198.

Cf. A348002, A348004.

Programs

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