A125732 Numbers n such that n=k*MiDi(n) for some integer k, where MiDi(n) = A103977(n) = "Minimal Difference of Divisors".

1, 2, 4, 8, 10, 16, 18, 32, 36, 44, 64, 72, 100, 128, 136, 144, 152, 162, 184, 196, 200, 256, 288, 324, 392, 400, 450, 512, 576, 648, 738, 748, 752, 784, 800, 882, 884, 900, 968, 1024, 1152, 1296, 1352, 1458, 1568, 1600, 1764, 1800, 1936, 2048, 2144, 2178, 2272

Offset

1,2

Comments

A000079 is a subsequence because for n equal to a power of 2 the definition is satisfied by choosing k=n.

Links

Amiram Eldar, Table of n, a(n) for n = 1..500

Mathematica

midi[n_] := Module[{d = Divisors[n], c, p, m}, c = CoefficientList[Product[1 + x^i, {i, d}], x]; p = -1 + Position[c, _?(# > 0 &)] // Flatten; m = Length[p]; If[OddQ[m], If[(d = p[[(m + 1)/2]] - p[[(m - 1)/2]]) == 1, 0, d], p[[m/2 + 1]] - p[[m/2]]]]; s = {}; Do[m = midi[n]; If[m > 0 && Divisible[n, m], AppendTo[s, n]], {n, 1, 2000}]; s (* Amiram Eldar, Dec 11 2019 *)

Crossrefs

Cf. A103977, A125733.

Sequence in context: A268497 A093886 A352203 * A032533 A062884 A026169

Adjacent sequences: A125729 A125730 A125731 * A125733 A125734 A125735

Keyword

nonn

Author

Yasutoshi Kohmoto, Jan 01 2007

Extensions

More terms from R. J. Mathar, Nov 27 2007

More terms from Amiram Eldar, Dec 11 2019

Status

approved