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 A237620 Semiperimeters s of primitive Pythagorean triples (a, b, c) where a, b, c and s are not squarefree. 0
 513, 1960, 2254, 2684, 3225, 3276, 3843, 3969, 4260, 4482, 4950, 5022, 5148, 5247, 5994, 6903, 7029, 7502, 7956, 8658, 10164, 10527, 12201, 12463, 12750, 12936, 13189, 13552, 13728, 13923, 15575, 15717, 16023, 16244, 16611, 16768 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS No primitive Pythagorean triangle (PPT) can have all its integer sides squarefree since at least one side must be divisible by 4. However it is possible to find PPT's where none of the integer sides and the semiperimeter are squarefree. a(n) is the ordered occurrences of such semiperimeters. LINKS EXAMPLE a(5)=3225 as the PPT (825, 2752, 2873) has a semiperimeter of 3225, no member of (825, 2752, 2873, 3225) is squarefree and it is the 5th occurrence of such a semiperimeter. MATHEMATICA getpairs[k_] := Reverse[Select[IntegerPartitions[k, {2}], GCD[#[[1]], #[[2]]]==1 &]]; getlist[j_] := (newlist=getpairs[j]; Table[{newlist[[m]][[1]]^2-newlist[[m]][[2]]^2, 2newlist[[m]][[1]]*newlist[[m]][[2]], newlist[[m]][[1]]^2+newlist[[m]][[2]]^2, newlist[[m]][[1]]*j}, {m, 1, Length[newlist]}]); p=100; quads={}; Do[AppendTo[quads, getlist[2n+1]], {n, 1, p}]; sqquads=Select[Flatten[quads, 1], Union@Table[SquareFreeQ@#[[r]], {r, 1, 4}]=={False} &]; lst=Table[sqquads[[k]][[4]], {k, 1, Length@sqquads}]; Select[Sort@lst, #<2 p^2 &] CROSSREFS Sequence in context: A182108 A066697 A076338 * A111344 A230188 A223651 Adjacent sequences:  A237617 A237618 A237619 * A237621 A237622 A237623 KEYWORD nonn AUTHOR Frank M Jackson, Feb 10 2014 STATUS approved

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Last modified January 24 15:36 EST 2022. Contains 350538 sequences. (Running on oeis4.)