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 A316834 Numbers with a unique representation as a sum of four distinct odd squares. 5
 84, 116, 140, 164, 180, 196, 212, 236, 244, 332, 460, 628 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers n that have a unique representation as n = h^2 + i^2 + j^2 + k^2 with h,i,j,k odd and 0 < h < i < j < k. No more terms up to 5*10^5. - Robert Israel, Jul 20 2018 a(13) > 5*10^6, if it exists. - Robert Price, Jul 25 2018 a(13) > 10^11, if it exists (which seems very unlikely). - Jon E. Schoenfield, Jul 28 2018 LINKS Michael D. Hirschhorn, The Power of q: A Personal Journey, Springer 2017. See Chapter 31: Partitions into Four Distinct Squares of Equal Parity. EXAMPLE 156 (a member of A316833) is not a member here since it has two representations: 156 = 1+25+49+81 = 1+9+25+121. MAPLE N:= 10000: # to get all terms <= N V:= Vector(N): for a from 1 to floor(sqrt(N/4)) by 2 do   for b from a+2 to floor(sqrt((N-a^2)/3)) by 2 do     for c from b+2 to floor(sqrt((N-a^2-b^2)/2)) by 2 do       for d from c + 2  by 2 do         r:= a^2+b^2+c^2+d^2;         if r > N then break fi;         V[r]:= V[r]+1 od od od od: select(r -> V[r]=1, [\$1..N]); # Robert Israel, Jul 20 2018 MATHEMATICA okQ[n_] := Count[PowersRepresentations[n, 4, 2], pr_List /; Union[pr] == pr && AllTrue[pr, OddQ]] == 1; Select[Range, okQ] (* Jean-François Alcover, Apr 02 2019 *) CROSSREFS Cf. A316833. Sequence in context: A209204 A219801 A316833 * A227734 A192322 A015708 Adjacent sequences:  A316831 A316832 A316833 * A316835 A316836 A316837 KEYWORD nonn,more AUTHOR N. J. A. Sloane, Jul 19 2018 STATUS approved

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Last modified June 1 20:49 EDT 2020. Contains 334765 sequences. (Running on oeis4.)