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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
OFFSET
1,1
COMMENTS
All terms are powerful (A001694).
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
KEYWORD
nonn
AUTHOR
Naohiro Nomoto, Sep 23 2000
EXTENSIONS
More terms from Jinyuan Wang, May 01 2021
STATUS
approved