A384098 a(n) is the least number that has exactly n distinct differences between its consecutive divisors (ordered by size).

2, 4, 8, 16, 28, 56, 60, 144, 120, 252, 210, 360, 480, 630, 720, 1008, 1344, 1320, 2040, 1680, 2160, 2520, 3276, 2640, 3360, 3960, 4680, 5280, 6600, 6720, 8580, 10080, 9360, 7920, 13440, 13200, 13860, 16380, 15840, 18720, 23400, 23760, 18480, 31920, 31680, 27720

Offset

1,1

Comments

a(n) is the least number k such that A060682(k) = n.

a(n) exists for all n since A060682(2^n) = n.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Formula

a(n) <= 2^n.

Mathematica

A060682[n_] := Length[Union[Differences[Divisors[n]]]];
seq[len_] := Module[{s = Table[0, {len}], c = 0, n = 2, i}, While[c < len, i = A060682[n]; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[50]

Prog

(PARI) A060682(n) = my(d=divisors(n)); #vecsort(vector(#d-1, k, d[k+1] - d[k]), , 8); \\ Michel Marcus at A060682
list(len) = {my(s = vector(len), c = 0, n = 2, i); while(c < len, i = A060682(n); if(i <= len && s[i] == 0, c++; s[i] = n); n++); s; }

Crossrefs

Cf. A060682, A384097.

Sequence in context: A318767 A208531 A349052 * A355969 A308542 A326116

Adjacent sequences: A384095 A384096 A384097 * A384099 A384100 A384101

Keyword

nonn

Author

Amiram Eldar, Sep 16 2025

Status

approved