A066213 Numbers which are sums of squares of some subset of divisors.

1, 4, 9, 16, 20, 25, 30, 36, 49, 64, 80, 81, 90, 100, 120, 121, 126, 130, 144, 150, 169, 180, 195, 196, 210, 225, 252, 256, 264, 270, 272, 280, 289, 294, 300, 315, 320, 324, 330, 336, 350, 360, 361, 378, 390, 396, 400, 414, 420, 441, 450, 468, 480, 484, 500

Offset

1,2

Comments

If m is in the sequence then so is m*k^2 for k >= 1. - David A. Corneth, Jan 22 2024

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

David A. Corneth, PARI program

Example

20 is in the list since 20 = 2^2 + 4^2 and 2 and 4 are divisors of 20

Maple

isA066213 := proc(n)
    local S, els;
    S:=subsets(numtheory[divisors](n));
    while not S[finished] do
        els:=S[nextvalue]() ;
        if add(d^2, d=els) = n then
            return true ;
        end if ;
    end do;
    false
end proc:
for n from 1 do
    if isA066213(n) then
        print(n) ;
    end if;
end do: # R. J. Mathar, Oct 09 2023

Mathematica

okQ[k_] := AnyTrue[Subsets[Select[Divisors[k]^2, # <= k&]], Total[#]==k&];
Reap[For[k = 1, k <= 5000, k++, If[okQ[k], Print[k]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, May 27 2024 *)

Prog

(PARI) \\ See PARI link

Crossrefs

Cf. A005835, A066214, A066215, A066216.

Sequence in context: A313332 A313333 A313334 * A355854 A010441 A046871

Adjacent sequences: A066210 A066211 A066212 * A066214 A066215 A066216

Keyword

nonn

Author

Erich Friedman, Dec 17 2001

Extensions

Offset 1 from David A. Corneth, Jan 22 2024

Status

approved