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A273109
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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.
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6
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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
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OFFSET
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1,2
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COMMENTS
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Is this also the union of 12 and the powers of 2?
All powers of 2 are in the sequence.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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