Felix Huber - cp's OEIS frontend

A386944 Long legs of Pythagorean triples of the form (u^2 - v^2, 2uv, u^2 + v^2), ordered by increasing hypotenuse (A386943).

8, 16, 24, 30, 32, 36, 48, 48, 42, 60, 70, 64, 80, 72, 96, 96, 90, 84, 108, 120, 100, 112, 126, 120, 110, 140, 135, 128, 160, 154, 168, 160, 144, 144, 192, 198, 192, 180, 182, 216, 224, 168, 216, 240, 196, 200, 234, 224, 252, 189, 240, 210, 286, 288, 220, 280, 280

Offset: 1

Felix Huber, Aug 24 2025

In the form (u^2 - v^2, 2*u*v, u^2 + v^2), u^2 + v^2 is the hypotenuse, max(u^2 - v^2, 2*u*v) is the long leg and min(u^2 - v^2, 2*u*v) is the short leg.

			The nonprimitive Pythagorean triple (6, 8, 10) is of the form (u^2 - v^2, 2*u*v, u^2 + v^2): From u = 3 and v = 1 follows u^2 - v^2 = 8 (long leg), 2*u*v = 6 (short leg), u^2 - v^2 = 10 (hypotenuse). Therefore, 8 is a term.

Felix Huber, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pythagorean Triple

Subsequence of A046084.

Cf. A046087, A366675, A380073, A386308, A386943, A386945.

A386944:=proc(N) # To get all hypotenuses <= N
    local i,l,u,v;
    l:=[];
    for u from 2 to floor(sqrt(N-1)) do
        for v to min(u-1,floor(sqrt(N-u^2))) do
            if gcd(u,v)>1 or is(u-v,even) then
                l:=[op(l),[u^2+v^2,max(2*u*v,u^2-v^2),min(2*u*v,u^2-v^2)]]
            fi
        od
    od;
    l:=sort(l);
    return seq(l[i,2],i=1..nops(l));
end proc;
A386944(296);

a(n) = sqrt(A386943(n)^2 - A386945(n)^2).

{A046084(n)} = {a(n)} union {A046087(n)} union {A386308(n)}.

A386945 Short legs of Pythagorean triples of the form (p^2 - q^2, 2pq, p^2 + q^2), ordered by increasing hypotenuse (A386943).

Original entry on oeis.org

6, 12, 10, 16, 24, 27, 14, 20, 40, 32, 24, 48, 18, 54, 28, 40, 56, 80, 45, 22, 75, 66, 32, 64, 96, 48, 72, 96, 36, 72, 26, 78, 108, 130, 56, 40, 80, 112, 120, 63, 30, 160, 90, 44, 147, 150, 88, 132, 64, 180, 128, 176, 48, 34, 192, 96, 102, 144, 170, 192, 125, 72

Offset: 1

Felix Huber, Aug 24 2025

In the form (u^2 - v^2, 2*u*v, u^2 + v^2), u^2 + v^2 is the hypotenuse, max(u^2 - v^2, 2*u*v) is the long leg and min(u^2 - v^2, 2*u*v) is the short leg.

			The nonprimitive Pythagorean triple (6, 8, 10) is of the form (u^2 - v^2, 2*u*v, u^2 + v^2): From u = 3 and v = 1 follows u^2 - v^2 = 8 (long leg), 2*u*v = 6 (short leg), u^2 - v^2 = 10 (hypotenuse). Therefore, 6 is a term.

Felix Huber, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pythagorean Triple

Subsequence of A046083.

Cf. A046086, A366674, A380074, A386309, A386943, A386944.

A386945:=proc(N) # To get all hypotenuses <= N
    local i,l,u,v;
    l:=[];
    for u from 2 to floor(sqrt(N-1)) do
        for v to min(u-1,floor(sqrt(N-u^2))) do
            if gcd(u,v)>1 or is(u-v,even) then
                l:=[op(l),[u^2+v^2,max(2*u*v,u^2-v^2),min(2*u*v,u^2-v^2)]]
            fi
        od
    od;
    l:=sort(l);
    return seq(l[i,3],i=1..nops(l));
end proc;
A386945(296);

a(n) = sqrt(A386943(n)^2 - A386944(n)^2).

{A046083(n)} = {a(n)} union {A046086(n)} union {A386309(n)}.

A386309 Short legs of Pythagorean triples that do not have the form (u^2 - v^2, 2uv, u^2 + v^2) ordered by increasing hypotenuse (A386307), where u and v are positive integers.

Original entry on oeis.org

9, 15, 18, 21, 15, 30, 24, 33, 36, 39, 25, 42, 45, 21, 30, 51, 40, 60, 35, 57, 60, 48, 63, 66, 36, 69, 56, 72, 27, 35, 78, 50, 81, 84, 55, 100, 87, 90, 42, 93, 60, 84, 99, 65, 102, 80, 120, 105, 49, 70, 33, 111, 60, 88, 114, 117, 99, 75, 48, 120, 140, 96, 123, 45

Offset: 1

Felix Huber, Aug 19 2025

In the form (u^2 - v^2, 2*u*v, u^2 + v^2), u^2 + v^2 is the hypotenuse, max(u^2 - v^2, 2*u*v) is the long leg and min(u^2 - v^2, 2*u*v) is the short leg.

			The Pythagorean triple (9, 12, 15) does not have the form (u^2 - v^2, 2*u*v, u^2 + v^2), because 15 is not a sum of two nonzero squares. Therefore 12 is a term.

Felix Huber, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pythagorean Triple

Subsequence of A046083.

Cf. A366674, A380074, A386307, A386308, A386945.

A386309:=proc(N) # To get all terms with hypotenuses <= N
    local i,l,m,u,v,r,x,y,z;
    l:={};
    m:={};
    for u from 2 to floor(sqrt(N-1)) do
        for v to min(u-1,floor(sqrt(N-u^2))) do
            x:=min(2*u*v,u^2-v^2);
            y:=max(2*u*v,u^2-v^2);
            z:=u^2+v^2;
            m:=m union {[z,y,x]};
            if gcd(u,v)=1 and is(u-v,odd) then
                l:=l union {seq([i*z,i*y,i*x],i=1..N/z)}
            fi
        od
    od;
    r:=l minus m;
    return seq(r[i,3],i=1..nops(r));
end proc;
A386309(1000);

a(n) = sqrt(A386307(n)^2 - A386308(n)^2).

{A046083(n)} = {a(n)} union {A046086(n)} union {A386945(n)}.

A386307 Ordered hypotenuses of Pythagorean triples that do not have the form (u^2 - v^2, 2uv, u^2 + v^2), where u and v are positive integers.

Original entry on oeis.org

15, 25, 30, 35, 39, 50, 51, 55, 60, 65, 65, 70, 75, 75, 78, 85, 85, 87, 91, 95, 100, 102, 105, 110, 111, 115, 119, 120, 123, 125, 130, 130, 135, 140, 143, 145, 145, 150, 150, 155, 156, 159, 165, 169, 170, 170, 174, 175, 175, 182, 183, 185, 185, 187, 190, 195, 195

Offset: 1

Felix Huber, Aug 13 2025

In the form (u^2 - v^2, 2*u*v, u^2 + v^2), u^2 + v^2) is the hypotenuse, max(u^2 - v^2, 2*u*v) is the long leg and min(u^2 - v^2, 2*u*v) is the short leg.
A101930(n) gives the total number of Pythagorean triples <= 10^n. The percentage of triangles in this sequence increases continuously:
               number of terms <= h     total number of
       h       in this sequence         hypotenuses <= h      percentage
      10                 0                    2                  0.0 %
     100                21                   52                 40.4 %
    1000               514                  881                 58.3 %
   10000              8629                12471                 69.2 %
  100000            122431               161436                 75.8 %

			The Pythagorean triple (9, 12, 15) does not have the form (u^2 - v^2, 2*u*v, u^2 + v^2), because 15 is not a sum of two nonzero squares. Therefore 15 is a term.

Felix Huber, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pythagorean Triple

Subsequence of A009000.

Cf. A101930, A366428, A380072, A386308, A386309, A386943.

A386307:=proc(N) # To get all hypotenuses <= N
    local i,l,m,u,v,r,x,y,z;
    l:={};
    m:={};
    for u from 2 to floor(sqrt(N-1)) do
        for v to min(u-1,floor(sqrt(N-u^2))) do
            x:=min(2*u*v,u^2-v^2);
            y:=max(2*u*v,u^2-v^2);
            z:=u^2+v^2;
            m:=m union {[z,y,x]};
            if gcd(u,v)=1 and is(u-v,odd) then
                l:=l union {seq([i*z,i*y,i*x],i=1..N/z)}
            fi
        od
    od;
    r:=l minus m;
    return seq(r[i,1],i=1..nops(r));
end proc;
A386307(1000);

a(n) = sqrt(A386308(n)^2 + A386309(n)^2).

{A009000(n)} = {a(n)} union {A020882(n)} union {A386943(n)}.

A386308 Long legs of Pythagorean triples that do not have the form (u^2 - v^2, 2uv, u^2 + v^2) ordered by increasing hypotenuse (A386307), where u and v are positive integers.

Original entry on oeis.org

12, 20, 24, 28, 36, 40, 45, 44, 48, 52, 60, 56, 60, 72, 72, 68, 75, 63, 84, 76, 80, 90, 84, 88, 105, 92, 105, 96, 120, 120, 104, 120, 108, 112, 132, 105, 116, 120, 144, 124, 144, 135, 132, 156, 136, 150, 126, 140, 168, 168, 180, 148, 175, 165, 152, 156, 168, 180

Offset: 1

Felix Huber, Aug 19 2025

In the form (u^2 - v^2, 2*u*v, u^2 + v^2), u^2 + v^2 is the hypotenuse, max(u^2 - v^2, 2*u*v) is the long leg and min(u^2 - v^2, 2*u*v) is the short leg.

			The Pythagorean triple (9, 12, 15) does not have the form (u^2 - v^2, 2*u*v, u^2 + v^2), because 15 is not a sum of two nonzero squares. Therefore 12 is a term.

Felix Huber, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pythagorean Triple

Subsequence of A046084.

Cf. A366675, A380073, A386307, A386309, A386944.

A386308:=proc(N) # To get all terms with hypotenuses <= N
    local i,l,m,u,v,r,x,y,z;
    l:={};
    m:={};
    for u from 2 to floor(sqrt(N-1)) do
        for v to min(u-1,floor(sqrt(N-u^2))) do
            x:=min(2*u*v,u^2-v^2);
            y:=max(2*u*v,u^2-v^2);
            z:=u^2+v^2;
            m:=m union {[z,y,x]};
            if gcd(u,v)=1 and is(u-v,odd) then
                l:=l union {seq([i*z,i*y,i*x],i=1..N/z)}
            fi
        od
    od;
    r:=l minus m;
    return seq(r[i,2],i=1..nops(r));
end proc;
A386308(1000);

a(n) = sqrt(A386307(n)^2 - A386309(n)^2).

{A046084(n)} = {a(n)} union {A046087(n)} union {A386944(n)}.

A386538 a(n) is the maximum possible area of a polygon within a circle of radius n, where both the center and the vertices lie on points of a unit square grid.

Original entry on oeis.org

0, 2, 8, 24, 42, 74, 104, 138, 186, 240, 304, 362, 424, 512, 594, 690, 776, 880, 986, 1104, 1232, 1346, 1490, 1624, 1762, 1930, 2088, 2256, 2418, 2594, 2784, 2962, 3170, 3368, 3584, 3810, 4008, 4248, 4466, 4730, 4976, 5210, 5474, 5736, 6024, 6306, 6570, 6864, 7154

Offset: 0

Felix Huber, Aug 05 2025

nonn

a(n) > 99% of the circle area for n >= 50.
Conjecture: The maximum possible area of a polygon within the circle would be the same if only the vertices but not the center were fixed on grid points.
All terms are even.

			See linked illustration of the term a(4) = 42.

Felix Huber, Table of n, a(n) for n = 0..10000
Felix Huber, Illustration of a(4) = 42
Eric Weisstein's World of Mathematics, Pick's Theorem

Cf. A000217, A066643, A123690, A125228, A288247, A322106, A322107, A357577, A386539.

A386538:=proc(n)
    local x,y,p,s;
    p:=4*n;
    s:={};
    for x to n do
        y:=floor(sqrt(n^2-x^2));
        p:=p+4*y;
        s:=s union {y}
    od;
    return p-2*nops(s)
end proc;
seq(A386538(n),n=0..48);

a[n_] := Module[{p=4n},s = {}; Do[ y = Floor[Sqrt[n^2 - x^2]];p = p + 4*y;s = Union[s, {y}],{x,n} ];p - 2*Length[s]];Array[a,49,0] (* James C. McMahon, Aug 19 2025 *)

a(n) = A386539(A000217(n)) = A386539(n,n) for n >= 1.

a(n) <= A066643(n).

A386539 Triangle read by rows: T(n,k) is the maximum possible area of a polygon within a ellipse with integer axis n and k, where n >= k >= 1 and both the center and the vertices lie on points of a unit square grid.

Original entry on oeis.org

2, 4, 8, 6, 14, 24, 8, 20, 28, 42, 10, 26, 38, 56, 74, 12, 32, 48, 66, 82, 104, 14, 38, 58, 80, 100, 122, 138, 16, 40, 64, 88, 114, 134, 164, 186, 18, 46, 74, 98, 132, 152, 186, 212, 240, 20, 52, 84, 112, 150, 174, 208, 232, 266, 304, 22, 58, 94, 126, 160, 196, 226, 262, 296, 324, 362

Offset: 1

Felix Huber, Aug 05 2025

The axes of the ellipse are assumed to be aligned with the coordinate axes.
Conjecture: The maximum possible area of a polygon within the ellipse would be the same if only the vertices but not the center were fixed on grid points.
All terms are even.

			The triangle T(n,k) begins:
   n\k  1   2   3   4   5   6   7   8   9  10  11 ...
   1:   2
   2:   4   8
   3:   6  14  24
   4:   8  20  28  42
   5:  10  26  38  56  74
   6:  12  32  48  66  82 104
   7:  14  38  58  80 100 122 138
   8:  16  40  64  88 114 134 164 186
   9:  18  46  74  98 132 152 186 212 240
  10:  20  52  84 112 150 174 208 232 266 304
  11:  22  58  94 126 160 196 226 262 296 324 362
 ...
See linked illustration of the term T(5,3) = 38.

Felix Huber, Rows n = 1..141 of triangle, flattened
Felix Huber, Illustraton of T(5,3) = 38
Eric Weisstein's World of Mathematics, Ellipse
Eric Weisstein's World of Mathematics, Pick's Theorem

Cf. A000217, A108126, A288247, A386539.

T386539:=proc(n,k)
    local x,y,p,s;
    p:=2*(n+k);
    s:={0};
    for x to n-1 do
        y:=floor(k*sqrt(1-x^2/n^2));
        p:=p+4*y;
        s:=s union {y}
    od;
    return p-2*nops(s)
end proc;
seq(seq(T386539(n,k),k=1..n),n=1..25);

T[n_, k_] := Module[{p=2*(n+k)},s = {0};Do[ y = Floor[k*Sqrt[1 - x^2/n^2]];p = p + 4*y;s = Union[s, {y}],{x,n-1}];p - 2*Length[s]];Flatten[Table[T[n, k], {n, 1, 11}, {k, 1, n}]] (* James C. McMahon, Aug 19 2025 *)

a(A000217(n)) = T(n,n) = A386538(n).

a(n) < Pi*n*k.

A386916 Nonprimes k such that sopfr(k) = rad(k), where sopfr(k) is sum of the prime factors of k (counting multiplicity), and rad(k) is the product of its distinct prime factors.

Original entry on oeis.org

18750, 22500, 24000, 27000, 28800, 30720, 32400, 34560, 36450, 38880, 43740, 201684, 345744, 388962, 526848, 592704, 666792, 903168, 1016064, 1143072, 1285956, 1376256, 1548288, 1741824, 1959552, 2204496, 2480058, 7730448, 8696754, 33732864, 35644128, 37949472

Offset: 1

Felix Huber, Aug 13 2025

nonn

Nonprimes k such that A001414(k) = A007947(k).
The nonprimes k in this sequence share the property sopfr(k) = rad(k) with the primes.
From Felix Huber and David A. Corneth, Aug 13 2025: (Start)
Terms have at least three distinct prime factors.
Proof: If a term had exactly 0 distinct prime factors then it is 1 but 1 is not a term.
If a term had exactly one distinct prime divisor then it is of the form p^m where p is prime. If m = 1 then it is excluded as it is prime. If m > 1 then sopfr(p^m) = m*p > p = rad(p^m) contradicting equality between sopfr(p^m) and rad(p^m).
If a term had exactly two distinct prime factors, p and q, then there would have to be positive integers x and y satisfying p*q = x*p + y*q, or equivalently, p*(q - x) = y*q. Since q divides neither p nor q - x, this is impossible; therefore, no term with exactly two distinct prime factors exists.
Terms with three and more distinct prime factors do exist completing the proof. (End)
Proper subset of A126706. - Michael De Vlieger, Aug 13 2025

			18750 = 2*3*5^5 is a term because 2 + 3 + 5 + 5 + 5 + 5 + 5 = 2*3*5 = 30.
1285956 = 2^2*3^8*7^2 is a term because 2 + 2 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 7 + 7 = 2*3*7 = 42.
18537438215625 = 3*5^5*7^11 is a term because 3 + 5*5 + 11*7 = 3*5*7 = 105.

David A. Corneth, Table of n, a(n) for n = 1..10344 (terms <= 10^35)

Subsequence of A018252.

Cf. A000040, A001414, A007947, A085718.

A386916:=proc(n)
    option remember;
    local k,i;
    if n=1 then
        18750
    else
        for k from procname(n-1)+1 do
            if not isprime(k) and NumberTheory:-Radical(k)=add(i[1]*i[2],i in ifactors(k)[2]) then
                return k
            fi
        od
    fi;
end proc;
seq(A386916(n),n=1..10);

q[k_] := !PrimeQ[k] && Module[{f = FactorInteger[k]},Plus @@ Times @@@f == Times @@ f[[;;, 1]]]; Select[Range[2, 10^6], q] (* Amiram Eldar, Aug 13 2025 *)

is(n) = {my(f = factor(n)); if(#f~ < 3, return(0)); prod(i = 1, #f~, f[i, 1]) == sum(i = 1, #f~, f[i,1]*f[i,2])} \\ David A. Corneth, Aug 13 2025

A385998 Numbers that are divisible by an equal number of distinct primes and squares.

Original entry on oeis.org

2, 3, 5, 7, 11, 12, 13, 17, 18, 19, 20, 23, 24, 28, 29, 31, 37, 40, 41, 43, 44, 45, 47, 50, 52, 53, 54, 56, 59, 61, 63, 67, 68, 71, 73, 75, 76, 79, 83, 88, 89, 92, 97, 98, 99, 101, 103, 104, 107, 109, 113, 116, 117, 124, 127, 131, 135, 136, 137, 139, 147, 148, 149

Offset: 1

Felix Huber, Aug 05 2025

nonn

The smallest term such that number of distinct primes = number of squares = k is:
  k = 1: 2,
  k = 2: 12,
  k = 3: 240,
  k = 4: 1260.

			12 is divisible by 2 distinct primes (2, 3) and by 2 squares (1, 4).

Felix Huber, Table of n, a(n) for n = 1..10000

Supersequence of A000040.

Cf. A000290, A001221, A046951.

c:=(n,d)->igcd(n,d)=d and igcd(n/d,d)=d:
b:=n->nops(select(k->c(n,k),[seq(1..n)])):
A385998:=proc(n)
    option remember;
    local k;
    if n=1 then
        2
    else
        for k from procname(n-1)+1 do
            if b(k)=NumberTheory:-Omega(k,'distinct') then
                return k
            fi
        od
    fi;
end proc;	
seq(A385998(n),n=1..63);

q[k_] := Module[{e = FactorInteger[k][[;; , 2]]}, k > 1 && Length[e] == Times @@ (1 + Floor[e/2])]; Select[Range[150], q] (* Amiram Eldar, Aug 05 2025 *)

isok(m) = my(d=divisors(m)); #select(isprime, d) == #select(issquare, d); \\ Michel Marcus, Aug 05 2025

A385997 a(n) is the smallest k such that the sum of the first k primes has exactly n prime factors, counting multiplicity.

Original entry on oeis.org

1, 3, 5, 9, 17, 11, 103, 119, 475, 237, 2661, 1481, 3045, 1567, 22019, 34907, 24995, 28173, 4915, 269225, 214183, 927571, 1085315, 9724983, 2567053, 4620383, 8827803, 38175467, 37167809, 98773463, 153124063, 257222427, 370283099, 24322477, 592786617

Offset: 1

Felix Huber, Jul 27 2025

a(n) is the smallest k such that A001222(A007504(k)) = A102862(k) = n.

a(34) = 24322477. - Robert Israel, Jul 29 2025

			a(2) = 3, because the sum of the first three primes 2 + 3 + 5 = 10 = 2*5 has exactly 2 prime factors. The sums of the first 1 or 2 primes (2 or 2 + 3 = 5) have only one prime factor.
a(5) = 17, because the sum of the first 17 primes (440 = 2^3*5*11) has exactly 5 prime factors. The sums of the first 1, 2, ..., 16 primes have either fewer or more than 5 prime factors.

Cf. A000040, A001222, A007504, A102862.

M:= 29: # for a(1) .. a(M)
V:= Vector(M):
t:= 0: p:= 1: count:= 0:
for i from 1 while count < M do
  p:= nextprime(p);
  t:= t + p;
  v:= numtheory:-bigomega(t);
  if v <= M and V[v] = 0 then V[v]:= i; count:= count+1 fi
od:
convert(V,list); # Robert Israel, Jul 29 2025

a[n_]:=Module[{k=1,ps=0},Until[PrimeOmega[ps]==n,ps=ps+Prime[k];k++];k-1];Array[a,20] (* James C. McMahon, Aug 05 2025 *)

from itertools import count
from sympy import factorint, nextprime
def A385997(n):
    p, c = 2, 0
    for k in count(1):
        c += p
        if sum(factorint(c).values())==n:
            return k
        p = nextprime(p) # Chai Wah Wu, Aug 08 2025

a(23)-a(30) from Robert Israel, Jul 29 2025
a(31) from Sean A. Irvine, Aug 05 2025
a(32)-a(34) from Chai Wah Wu, Aug 08 2025
a(35) from Chai Wah Wu, Sep 01 2025

cp's OEIS Frontend

User: Felix Huber

A386944 Long legs of Pythagorean triples of the form (u^2 - v^2, 2*u*v, u^2 + v^2), ordered by increasing hypotenuse (A386943).

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A386945 Short legs of Pythagorean triples of the form (p^2 - q^2, 2*p*q, p^2 + q^2), ordered by increasing hypotenuse (A386943).

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A386309 Short legs of Pythagorean triples that do not have the form (u^2 - v^2, 2*u*v, u^2 + v^2) ordered by increasing hypotenuse (A386307), where u and v are positive integers.

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A386307 Ordered hypotenuses of Pythagorean triples that do not have the form (u^2 - v^2, 2*u*v, u^2 + v^2), where u and v are positive integers.

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A386308 Long legs of Pythagorean triples that do not have the form (u^2 - v^2, 2*u*v, u^2 + v^2) ordered by increasing hypotenuse (A386307), where u and v are positive integers.

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A386538 a(n) is the maximum possible area of a polygon within a circle of radius n, where both the center and the vertices lie on points of a unit square grid.

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Maple

Mathematica

Formula

A386539 Triangle read by rows: T(n,k) is the maximum possible area of a polygon within a ellipse with integer axis n and k, where n >= k >= 1 and both the center and the vertices lie on points of a unit square grid.

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Maple

Mathematica

A386944 Long legs of Pythagorean triples of the form (u^2 - v^2, 2uv, u^2 + v^2), ordered by increasing hypotenuse (A386943).

A386945 Short legs of Pythagorean triples of the form (p^2 - q^2, 2pq, p^2 + q^2), ordered by increasing hypotenuse (A386943).

A386309 Short legs of Pythagorean triples that do not have the form (u^2 - v^2, 2uv, u^2 + v^2) ordered by increasing hypotenuse (A386307), where u and v are positive integers.

A386307 Ordered hypotenuses of Pythagorean triples that do not have the form (u^2 - v^2, 2uv, u^2 + v^2), where u and v are positive integers.

A386308 Long legs of Pythagorean triples that do not have the form (u^2 - v^2, 2uv, u^2 + v^2) ordered by increasing hypotenuse (A386307), where u and v are positive integers.