A228004 Prime powers p^m with m >= 2 which are not the sum of consecutive cubes.

4, 16, 25, 32, 49, 81, 121, 128, 169, 243, 256, 289, 361, 529, 625, 841, 961, 1024, 1369, 1681, 1849, 2048, 2187, 2209, 2401, 2809, 3125, 3481, 3721, 4489, 5041, 5329, 6241, 6561, 6889, 7921, 8192, 9409, 10201, 10609, 11449, 11881, 12769, 14641, 16129

Offset: 1

Author

Arkadiusz Wesolowski, Aug 07 2013

Keywords

• nonn

Examples

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10137
• K. S. Brown, Sum of Consecutive Nth Powers Equals an Nth Power
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 97

Crossrefs

Cf. A025475, A217843.

Programs

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];