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Numbers that are sums of consecutive square pyramidal numbers.
7

%I #23 Dec 21 2018 08:35:53

%S 0,1,5,6,14,19,20,30,44,49,50,55,85,91,99,104,105,140,146,176,190,195,

%T 196,204,231,285,286,316,330,335,336,344,385,435,489,490,506,520,534,

%U 539,540,629,650,670,720,775,805,819,824,825,874,891,1014,1015,1105,1156,1160,1176,1190

%N Numbers that are sums of consecutive square pyramidal numbers.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SquarePyramidalNumber.html">Square Pyramidal Number</a>

%t anmax = 1000; nmax = Floor[(3*anmax)^(1/3)] + 1; Select[Union[Flatten[Table[Sum[k*(k + 1)*(2*k + 1)/6, {k, i, j}], {i, 0, nmax}, {j, i, nmax}]]], # <= anmax &] (* _Vaclav Kotesovec_, Dec 21 2018 *)

%Y Cf. A000330, A034705, A322468.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Dec 19 2018