A057371 Numbers k that can be expressed as k = w+x = y*z with w*x = k*(y+z) where w, x, y, and z are all positive integers.

64, 72, 81, 100, 108, 125, 128, 216, 225, 288, 324, 500, 576, 864, 972, 1125, 1152, 1225, 1800, 2025, 2700, 3125, 3200, 3528, 4500, 7776, 8100, 10125, 13068, 13689, 15488, 17496, 18496, 21125, 24500, 28800, 34848, 42336, 44100, 48672, 55225, 69696, 93636, 95256

Offset: 1

Author

Naohiro Nomoto, Sep 23 2000

Keywords

• nonn

Comments

All terms are powerful (A001694).

Examples

			64 is a term because a solution exists at k=64, w=32, x=32, y=8, z=8:
             k =  w + x  = y*z   with    w*x  =  k*(y+z)
becomes
            64 = 32 + 32 = 8*8   with   32*32 = 64*(8+8).
		

Crossrefs

Cf. A001694, A057369, A057370, A057372, A057373, A057421.

Programs

PARI

is(k) = fordiv(k, y, if(issquare(k^2 - 4*k*(y+k/y)), return(1))); 0; \\ Jinyuan Wang, May 01 2021

Extensions

More terms from Jinyuan Wang, May 01 2021