OFFSET
1,1
COMMENTS
If m is a term of A337988 then k^2*m is another term for any k in N*; so, there exist primitive terms m as 20, 90, 272,... in the sense that m' is not a term for any m' = m/k^2, k>1.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..637
EXAMPLE
20 = 2^2 + 4^2 and there is no k>1 such that 20/k^2 is another term, so 20 is in the sequence.
90 = 3^2 + 9^2 and there is no k>1 such that 90/k^2 is another term, so 90 is in the sequence.
468 = 12^2 + 18^2 and there is no k>1 such that 468/k^2 is another term, so 468 is in the sequence.
MATHEMATICA
sumdivQ[n_] := AnyTrue[Most @ Divisors[n], (s = n - #^2) > 0 && s != n/2 && IntegerQ@Sqrt[s] && Divisible[n, Sqrt[s]] &]; s = Select[Range[200000], sumdivQ]; seq = {s[[1]]}; Do[If[! AnyTrue[s[[1 ;; k - 1]], IntegerQ@Sqrt[s[[k]]/#] &], AppendTo[seq, s[[k]]]], {k, 2, Length[s]}]; seq (* Amiram Eldar, Oct 31 2020 *)
PROG
(PARI) isok(m) = {my(d=divisors(m)); for (i=2, #d, for (j=1, i-1, if (d[i]^2+d[j]^2 == m, return (1)); ); ); } \\ A337988
isprim(x, vp) = {for (i=1, #vp, my(y = x/vp[i]); if ((denominator(y)==1) && issquare(y), return (0)); ); return(1); }
lista(nn) = {my(vp = []); for (n=1, nn, if (isok(n) && isprim(n, vp), vp = concat(vp, n)); ); vp; } \\ Michel Marcus, Oct 30 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Oct 30 2020
EXTENSIONS
More terms from Michel Marcus, Oct 30 2020
STATUS
approved