A228004 - OEIS

%I #27 Apr 03 2023 10:36:13

%S 4,16,25,32,49,81,121,128,169,243,256,289,361,529,625,841,961,1024,

%T 1369,1681,1849,2048,2187,2209,2401,2809,3125,3481,3721,4489,5041,

%U 5329,6241,6561,6889,7921,8192,9409,10201,10609,11449,11881,12769,14641,16129

%N Prime powers p^m with m >= 2 which are not the sum of consecutive cubes.

%H Chai Wah Wu, <a href="/A228004/b228004.txt">Table of n, a(n) for n = 1..10137</a>

%H K. S. Brown, <a href="http://www.mathpages.com/home/kmath147.htm">Sum of Consecutive Nth Powers Equals an Nth Power</a>

%H G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/24463.html">Prime Curios! 97</a>

%e 9 is not in the sequence since it is equal to 1^3 + 2^3.

%o (Magma) lst:=[]; r:=26; c:=r^3; for n in [2..r] do for m in [n-1..0 by -1] do s:=((n^2+n)^2-(m^2+m)^2)/4; if s gt c then break; end if; if not s in lst then Append(~lst, s); end if; end for; end for; lst:=Sort(lst); [p: p in [2..c] | not IsPrime(p) and IsPrimePower(p) and not p in lst];

%Y Cf. A025475, A217843.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Aug 07 2013