

A115783


Numbers that can be represented in the form (m+1)^k  m^k in at least two ways.


1



0, 1, 7, 15, 19, 31, 37, 61, 63, 65, 91, 127, 169, 175, 211, 217, 255, 271, 331, 369, 397, 469, 511, 547, 631, 665, 671, 721, 781, 817, 919, 1023, 1027, 1105, 1141, 1261, 1387, 1519, 1657, 1695, 1801, 1951, 2047, 2059, 2101, 2107, 2269, 2437, 2465, 2611, 2791
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OFFSET

1,3


COMMENTS

It is easy to see that all the terms of A003215 also belong to this sequence (thus infinite), since they can be represented as (p+1)^2  p^2 and as (q+1)^3  q^3.  Giovanni Resta, Feb 15 2006


LINKS



MATHEMATICA

t = {}; Do[a = (m + 1)^k  m^k; If[a < 3000, AppendTo[t, a]], {m, 3000}, {k, 23}]; t = Split@ Sort@ t; Union@ Flatten@ t[[Select[ Range@1500, Length@t[[ # ]] > 1 &]]] (* Robert G. Wilson v, Feb 08 2006 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



