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A024796
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Numbers expressible in more than one way as i^2 + j^2 + k^2, where 1 <= i <= j <= k.
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24
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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MATHEMATICA
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okQ[n_]:= Length[Select[PowersRepresentations[n, 3, 2], !MemberQ[#, 0] &]] > 1; (* Jinyuan Wang, Feb 12 2019 *)
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PROG
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(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
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CROSSREFS
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Cf. A000408, A007692, A008917, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025367, A025427.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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