# [seqfan] About A090503 Number of hyperplanes

Jean-François Alcover jf.alcover at gmail.com
Wed Nov 20 16:16:10 CET 2013

```Dear SeqFans,

While checking A090503 (without knowing anything about the subject)
I spotted missing terms, assuming the formula meant "All numbers of the
form".
For instance 127 = ((2^1)^(6 + 1) - 1)/(2^1 - 1) is missing,
though 63 = ((2^1)^(5 + 1) - 1)/(2^1 - 1) is present.
Same trouble with 255, 511, 1023, 1093, 2047, 3280, 4095, ...
I presume the formula actually meant "Some numbers of the form".
Any idea?

J.-F. Alcover

p.s. This is the way I did it with Mma:

f[n_] := Do[If[n == ( (p^m)^(d + 1) - 1)/( p^m - 1), Print[{n, d, m, p}];
Return[True]], {d, 2, 11}, {m, 1, 6}, {p, Prime /@ Range[18]}]

Select[Range[200], f[#] === True &]

{7,2,1,2}

{13,2,1,3}

{15,3,1,2}

{21,2,2,2}

{31,2,1,5}

{40,3,1,3}

{57,2,1,7}

{63,5,1,2}

{73,2,3,2}

{85,3,2,2}

{91,2,2,3}

{121,4,1,3}

{127,6,1,2}

{133,2,1,11}

{156,3,1,5}

{183,2,1,13}

{7, 13, 15, 21, 31, 40, 57, 63, 73, 85, 91, 121, 127, 133, 156, 183}
```