A254836 Numbers n expressible as a product of 4 factors in two different ways, n = a*b*c*d = x*y*w*z, with a+b+c+d = x+y+w+z.

36, 40, 48, 72, 80, 90, 96, 108, 120, 126, 144, 160, 168, 176, 180, 192, 200, 216, 225, 234, 240, 252, 270, 280, 288, 297, 300, 320, 324, 336, 352, 360, 378, 384, 396, 400, 405, 408, 420, 432, 440, 448, 450, 456, 468, 480

Offset: 1

Author

Carmine Suriano, Feb 08 2015

Keywords

• nonn

Comments

The first few terms have a+b+c+d = w+x+y+z equal to 14, 15, 12, 15, 16, 17, 15, ..., . - Robert G. Wilson v, Feb 09 2015

Examples

			40 is in the list since 40 = 1*1*5*8 = 1*2*2*10 and 1+1+5+8 = 15 = 1+2+2+10.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1114 (first 157 terms from Carmine Suriano)

Crossrefs

Cf. A060292.

Programs

Mathematica

fQ[n_] := If[ PrimeOmega@ n > 3, Block[{k = 1}, While[k < n && Length@ Select[ IntegerPartitions[k, {4}, Divisors@ n], Times @@ # == n &] < 2, k++]; If[k < 2n, True]]]; k = 1; lst = {}; While[k < 500, If[ fQ@ k, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Feb 09 2015 *)