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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 25 10:19 EST 2022. Contains 350565 sequences. (Running on oeis4.)