A369333 -id:A369333 - cp's OEIS frontend

A369334 Positive integers m such that there exist distinct pairs (a,b) and (c,d) with a <= b, c <= d, gcd(a,b,c,d) = 1, and m = ab(c+d) = (a+b)cd.

72, 144, 168, 360, 450, 480, 864, 990, 1200, 1404, 1568, 1600, 1800, 2040, 2160, 2520, 2646, 3150, 3360, 3600, 3780, 4050, 4800, 5184, 5400, 5520, 5880, 5940, 6720, 7056, 7200, 7350, 7800, 7938, 8550, 8640, 8694, 8712, 8976, 9408, 9450, 9504, 10416, 11550, 11760, 12000, 12600, 12960, 13230, 14112, 14850, 15288, 16128, 16200, 16560, 16562, 17640, 18000, 18144, 18216

Offset: 1

Max Alekseyev, Jan 20 2024

nonn

Note that a*b*(c+d) = (a+b)*c*d is equivalent to 1/a + 1/b = 1/c + 1/d.

Cf. A369333.

A371721 Numbers representable in the form uv(u+v) for u >= v >= 0 in at least two ways.

Original entry on oeis.org

0, 30, 210, 240, 390, 420, 462, 810, 880, 1008, 1020, 1056, 1122, 1190, 1482, 1680, 1920, 1980, 2070, 2100, 2310, 2970, 3120, 3360, 3696, 3750, 4160, 4290, 4320, 4830, 4914, 5460, 5670, 6006, 6090, 6270, 6480, 6630, 7040, 7380, 7440, 7770, 8064, 8160, 8190, 8448, 8580, 8976, 9120, 9240, 9520, 9900, 10290, 10530, 10640, 11340, 11856, 12210, 12432, 12474, 13110

Offset: 1

Max Alekseyev, Apr 04 2024

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Subsequence of A088915.

Cf. A369333, A369334.

N:= 10^5: # for terms <= N
V:= Vector(N):
for v from 1 while 2*v^3 <= N do
  for u from v do
    x:= u*v*(u+v);
    if x > N then break fi;
    V[x]:= V[x]+1
od od:
[0,op(select(t -> V[t] >= 2, [$1..N]))]; # Robert Israel, Dec 15 2024

cp's OEIS Frontend

A369334 Positive integers m such that there exist distinct pairs (a,b) and (c,d) with a <= b, c <= d, gcd(a,b,c,d) = 1, and m = ab(c+d) = (a+b)cd.

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A371721 Numbers representable in the form uv(u+v) for u >= v >= 0 in at least two ways.

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Author

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Maple

cp's OEIS Frontend

A369334 Positive integers m such that there exist distinct pairs (a,b) and (c,d) with a <= b, c <= d, gcd(a,b,c,d) = 1, and m = a*b*(c+d) = (a+b)*c*d.

Views

Author

Keywords

Comments

Crossrefs

A371721 Numbers representable in the form u*v*(u+v) for u >= v >= 0 in at least two ways.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

A369334 Positive integers m such that there exist distinct pairs (a,b) and (c,d) with a <= b, c <= d, gcd(a,b,c,d) = 1, and m = ab(c+d) = (a+b)cd.

A371721 Numbers representable in the form uv(u+v) for u >= v >= 0 in at least two ways.