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 A094942 Numbers having a unique partition into three squares. 19
 0, 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 14, 16, 19, 20, 21, 22, 24, 30, 32, 35, 37, 40, 42, 43, 44, 46, 48, 52, 56, 58, 64, 67, 70, 76, 78, 80, 84, 88, 91, 93, 96, 115, 120, 128, 133, 140, 142, 148, 160, 163, 168, 172, 176, 184, 190, 192, 208, 224, 232, 235 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Note that squares are allowed to be zero. From Wolfdieter Lang, Apr 09 2013: (Start) These are the numbers for which A000164(a(n)) = 1. a(n) is the n-th largest number which has a representation as a sum of three squares (square 0 allowed), in exactly one way, if neither the order of terms nor the signs of the numbers to be squared are taken into account. The multiplicity with order and signs taken into account are A005875(a(n)). These numbers are a proper subset of A000378. (End) Note that all these numbers are 4^k * A094739(n) for some k >= 0. - T. D. Noe, Nov 08 2013 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 FORMULA The sequence gives the increasingly ordered members of the set {m integer | A000164(m) = 1, m >= 0}. EXAMPLE From Wolfdieter Lang, Apr 09 2013 (Start) a(1) = 0 because 0 = 0^2 + 0^2 + 0^2 and 0 is the first number m with A000164(m)=1. a(8) = 8 = 0^2 + 2^2 + 2^2, the 8th largest number m for which A000164(m) is 1. (End) MATHEMATICA lim=25; nLst=Table[0, {lim^2}]; Do[n=a^2+b^2+c^2; If[n>0 && n

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Last modified November 30 20:17 EST 2021. Contains 349425 sequences. (Running on oeis4.)