A384097 a(n) is the least number that has exactly n divisors and the differences between its consecutive divisors (ordered by size) are distinct.

1, 2, 4, 8, 16, 28, 64, 88, 196, 176, 1024, 352, 4096, 704, 1936, 1408, 65536, 2816, 262144, 5104, 7744, 11264, 4194304, 15488, 234256, 45056, 30976, 34112, 268435456, 61952, 1073741824, 68224, 123904, 720896, 937024, 136448, 68719476736, 2883584, 495616, 272896

Offset

1,2

Comments

a(n) is the least term in A060683 that has n divisors.

Since 2^n is a term in A060683 for all n >= 0 and A000005(2^n) = n+1, then a(n) exists for all n.

Links

Table of n, a(n) for n=1..40.

Formula

a(n) <= 2^(n-1).

a(p) = 2^(p-1) for a prime p.

Mathematica

q[n_] := UnsameQ @@ Differences[Divisors[n]]; seq[len_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len, i = DivisorSigma[0, n]; If[i <= len && s[[i]] == 0 && q[n], c++; s[[i]] = n]; n++]; s]; seq[20]

Prog

(PARI) isA060683(k) = my(d=divisors(k)); #Set(vector(#d-1, k, d[k+1]-d[k])) == #d-1; \\ Michel Marcus at A060683
list(len) = {my(s = vector(len), c = 0, n = 1, i); while(c < len, i = numdiv(n); if(i <= len && s[i] == 0 && isA060683(n), c++; s[i] = n); n++); s; }

Crossrefs

Cf. A000005, A060680, A060681, A060682, A060683, A384098.

Sequence in context: A348413 A355968 A177269 * A018726 A049884 A085583

Adjacent sequences: A384094 A384095 A384096 * A384098 A384099 A384100

Keyword

nonn

Author

Amiram Eldar, Sep 16 2025

Status

approved