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

1,1

Comments

All terms are powerful (A001694).

Links

Table of n, a(n) for n=1..44.

Example

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).

Prog

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

Crossrefs

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

Sequence in context: A095533 A044864 A162528 * A045286 A334825 A057372

Adjacent sequences: A057368 A057369 A057370 * A057372 A057373 A057374

Keyword

nonn

Author

Naohiro Nomoto, Sep 23 2000

Extensions

More terms from Jinyuan Wang, May 01 2021

Status

approved