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.

1, 2, 4, 8, 12, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592

Offset

1,2

Comments

Is this also the union of 12 and the powers of 2?

All powers of 2 are in the sequence.

Links

Table of n, a(n) for n=1..35.

Example

For n = 12 the difference triangle of the divisors of 12 is
1 . 2 . 3 . 4 . 6 . 12
. 1 . 1 . 1 . 2 . 6
. . 0 . 0 . 1 . 4
. . . 0 . 1 . 3
. . . . 1 . 2
. . . . . 1
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.
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.

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A000079, A027750, A187202, A273102, A273103.

Sequence in context: A324214 A371732 A368507 * A046843 A376256 A373728

Adjacent sequences: A273106 A273107 A273108 * A273110 A273111 A273112

Keyword

nonn

Author

Omar E. Pol, May 15 2016

Extensions

a(12)-a(21) from Michel Marcus, May 16 2016

a(22)-a(35) from Amiram Eldar, Feb 23 2019

Status

approved