A125732 - OEIS

%I #9 Dec 11 2019 05:05:20

%S 1,2,4,8,10,16,18,32,36,44,64,72,100,128,136,144,152,162,184,196,200,

%T 256,288,324,392,400,450,512,576,648,738,748,752,784,800,882,884,900,

%U 968,1024,1152,1296,1352,1458,1568,1600,1764,1800,1936,2048,2144,2178,2272

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

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

%H Amiram Eldar, <a href="/A125732/b125732.txt">Table of n, a(n) for n = 1..500</a>

%t 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 *)

%Y Cf. A103977, A125733.

%K nonn

%O 1,2

%A _Yasutoshi Kohmoto_, Jan 01 2007

%E More terms from _R. J. Mathar_, Nov 27 2007

%E More terms from _Amiram Eldar_, Dec 11 2019