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
Keywords
Examples
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.
Programs
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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 *) -
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
Extensions
a(12)-a(21) from Michel Marcus, May 16 2016
a(22)-a(35) from Amiram Eldar, Feb 23 2019
Comments