A024796 - OEIS

A024796

Numbers expressible in more than one way as i^2 + j^2 + k^2, where 1 <= i <= j <= k.

27, 33, 38, 41, 51, 54, 57, 59, 62, 66, 69, 74, 75, 77, 81, 83, 86, 89, 90, 94, 98, 99, 101, 102, 105, 107, 108, 110, 113, 114, 117, 118, 121, 122, 123, 125, 126, 129, 131, 132, 134, 137, 138, 139, 141, 146, 147, 149, 150, 152, 153, 154, 155, 158, 161, 162, 164, 165, 166, 170

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

a(n) multiplied by (h^2)/(8*m*a^2) is the n-th energy level exhibiting accidental degeneracy, for a quantum mechanical particle of mass m in a cubic box of side length a (h is Planck's constant). - A. Timothy Royappa, Feb 12 2019

LINKS

Robert Price, Table of n, a(n) for n = 1..8057

FORMULA

{n: A025427(n) > 1 }. - R. J. Mathar, Aug 05 2022

MATHEMATICA

okQ[n_]:= Length[Select[PowersRepresentations[n, 3, 2], !MemberQ[#, 0] &]] > 1; (* Jinyuan Wang, Feb 12 2019 *)

PROG

(PARI) is(n)=if(n<27, return(0)); if(n%4==0, return(is(n/4))); my(w); for(i=sqrtint((n-1)\3)+1, sqrtint(n-2), my(t=n-i^2); for(j=sqrtint((t-1)\2)+1, min(sqrtint(t-1), i), if(issquare(t-j^2), w++>1 && return(1)))); 0 \\ Charles R Greathouse IV, Aug 05 2024

CROSSREFS

Cf. A000408, A007692, A008917, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025367, A025427.

Sequence in context: A173136 A030134 A290842 * A025322 A151742 A304243

Adjacent sequences: A024793 A024794 A024795 * A024797 A024798 A024799

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved