A288631 - OEIS

%I #10 Feb 16 2025 08:33:47

%S 2,6,10,15,19,28,31,35,44,56,60,69,85,92,96,105,110,121,141,145,146,

%T 154,170,182,195,205,209,218,231,234,259,280,286,290,295,299,315,340,

%U 344,376,386,390,399,408,415,425,440,476,489,507,511,520,525,536,561,570,589,597,646,651,655,664,670,680

%N Numbers that are the sum of two nonzero square pyramidal numbers (A000330).

%H Robert Israel, <a href="/A288631/b288631.txt">Table of n, a(n) for n = 1..10000</a>

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

%H <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>

%p M:= 20: # to get all terms <= A000330(M)

%p sqp:= [seq(k*(k+1)*(2*k+1)/6, k=1..M)]:

%p sort(convert(select(`<=`, {seq(seq(sqp[i]+sqp[j], j=1..i),i=1..M-1)},sqp[M]),list)); # _Robert Israel_, Jun 12 2017

%t nmax = 700; f[x_] := Sum[x^(k (k + 1) (2 k + 1)/6), {k, 1, 20}]^2; Exponent[#, x] & /@ List @@ Normal[Series[f[x], {x, 0, nmax}]]

%Y Cf. A000330, A000404, A020756, A051533, A102795.

%K nonn,changed

%O 1,1

%A _Ilya Gutkovskiy_, Jun 12 2017