cp's OEIS Frontend

A273109 Numbers n such that in the difference triangle of the divisors of n (including the divisors of n) the diagonal from the bottom entry to n gives the divisors of n.

%I A273109 #41 Feb 23 2019 08:00:34
%S A273109 1,2,4,8,12,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,
%T A273109 65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,
%U A273109 33554432,67108864,134217728,268435456,536870912,1073741824,2147483648,4294967296,8589934592
%N A273109 Numbers n such that in the difference triangle of the divisors of n (including the divisors of n) the diagonal from the bottom entry to n gives the divisors of n.
%C A273109 Is this also the union of 12 and the powers of 2?
%C A273109 All powers of 2 are in the sequence.
%e A273109 For n = 12 the difference triangle of the divisors of 12 is
%e A273109 1 . 2 . 3 . 4 . 6 . 12
%e A273109 . 1 . 1 . 1 . 2 . 6
%e A273109 . . 0 . 0 . 1 . 4
%e A273109 . . . 0 . 1 . 3
%e A273109 . . . . 1 . 2
%e A273109 . . . . . 1
%e A273109 The bottom entry is 1, and the diagonal from the bottom entry to 12 is [1, 2, 3, 4, 6, 12] hence the diagonal gives the divisors of 12, so 12 is in the sequence.
%e A273109 Note that for n = 12 and the powers of 2 the descending diagonals, from left to right, are symmetrics, for example: the first diagonal is 1, 1, 0, 0, 1, 1.
%t A273109 aQ[n_] := Module[{d=Divisors[n]}, nd = Length[d]; vd = d; ans = True; Do[ vd = Differences[vd]; If[Max[vd] != d[[nd-k]], ans=False; Break[]], {k,1,nd-1}]; ans]; Select[Range[100000], aQ] (* _Amiram Eldar_, Feb 23 2019 *)
%o A273109 (PARI) isok(n) = {my(d = divisors(n)); my(nd = #d); my(vd = d); for (k=1, nd-1, vd = vector(#vd-1, j, vd[j+1] - vd[j]); if (vecmax(vd) != d[nd-k], return (0));); return (1);} \\ _Michel Marcus_, May 16 2016
%Y A273109 Cf. A000079, A027750, A187202, A273102, A273103.
%K A273109 nonn
%O A273109 1,2
%A A273109 _Omar E. Pol_, May 15 2016
%E A273109 a(12)-a(21) from _Michel Marcus_, May 16 2016
%E A273109 a(22)-a(35) from _Amiram Eldar_, Feb 23 2019