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A124967 Numbers which can be expressed as the ordered sum of 3 squares in 3 or more different ways. 8
41, 50, 54, 65, 66, 74, 81, 86, 89, 90, 98, 99, 101, 110, 113, 114, 117, 121, 122, 125, 126, 129, 131, 134, 137, 145, 146, 149, 150, 153, 161, 162, 164, 166, 169, 170, 171, 173, 174, 178, 179, 181, 182, 185, 186, 189, 194, 197, 198, 200, 201, 205, 206, 209 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1) = 41 because 41 = 4^2+4^2+3^2 or 5^2+4^2+0^2 or 6^2+2^2+1^2.

117=0^2+6^2+9^2=1^2+4^2+10^2=2^2+7^2+8^2, so 117 is in the list.

MAPLE

b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i^2<n, 0,

      `if`(b(n, i-1, t)>3, 3, min(3, b(n, i-1, t)+

      `if`(i^2>n, 0, b(n-i^2, i, t-1))))))

    end:

a:= proc(n) option remember; local k;

      for k from 1 +`if`(n=1, 0, a(n-1))

      while b(k, isqrt(k), 3)<3 do od; k

    end:

seq(a(n), n=1..100);  # Alois P. Heinz, Apr 10 2013

MATHEMATICA

Select[Range[210], Length@PowersRepresentations[#, 3, 2] >= 3 &] (* Ray Chandler, Oct 31 2019 *)

PROG

(PARI) isA124967(n)={ local(cnt=0, z2) ; for(x=0, floor(sqrt(n)), for(y=x, floor(sqrt(n-x^2)), z2=n-x^2-y^2 ; if( z2>=y^2 && issquare(z2), cnt++ ; ) ; if(cnt >=3, return(1) ) ; ) ; ) ; return(0) ; } { for(n=1, 200, if( isA124967(n), print1(n, ", ") ; ) ; ) ; } (Mathar)

CROSSREFS

Cf. A124966-A124971.

Sequence in context: A039383 A043206 A043986 * A224443 A261259 A168348

Adjacent sequences:  A124964 A124965 A124966 * A124968 A124969 A124970

KEYWORD

nonn

AUTHOR

Artur Jasinski, Nov 14 2006

EXTENSIONS

Corrected and extended by Ray Chandler and R. J. Mathar, Nov 29 2006

STATUS

approved

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Last modified November 28 16:34 EST 2021. Contains 349413 sequences. (Running on oeis4.)