A371968 Numbers k that are not the sum of distinct squares that do not divide k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 39, 40, 42, 43, 44, 46, 47, 48, 50, 51, 54, 55, 56, 57, 59, 60, 63, 64, 66, 67, 68, 71, 72, 75, 76, 79, 80, 82, 84, 88, 91, 92, 95, 96, 99, 104, 107, 108, 111, 112, 120, 124, 127, 128, 132, 135, 140, 144, 147, 148, 156, 160, 168, 172, 176, 184, 188, 192, 200, 216, 224, 252, 256, 288, 300, 432

Offset: 1

Author

Robert Israel, Apr 15 2024

Keywords

• nonn

Comments

Numbers k such that A294266(k) = 0.

No other terms <= 100000.

Examples

			a(20) = 21 is a term because the only way to write 21 as the sum of distinct squares is 1^2 + 2^2 + 4^2, but 21 is divisible by 1^2.
		

Crossrefs

Cf. A294266.

Programs

Maple

filter:= proc(n) local P,k,x;
P:= 1;
for k from 2 to floor(sqrt(n)) do
  if n mod k^2 = 0 then next fi;
  P:= series(P*(1+x^(k^2)),x,n+1);
  if coeff(P,x,n) > 0 then return false fi;
od;
true
end proc:
select(filter, [$1..500]);

Extensions

More terms than usual in the DATA section, because these are probably all the terms.