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A134608
Composite numbers such that the cube root of the sum of cubes of their prime factors is an integer.
20
256, 588, 693, 3840, 6561, 14157, 17787, 141960, 178360, 313600, 337365, 350000, 387072, 390625, 407442, 432000, 466560, 531674, 535815, 541310, 664909, 697851, 1044582, 1262056, 1264640, 1299272, 1374327, 1547570, 1608575, 1660360
OFFSET
1,1
LINKS
EXAMPLE
a(3)=693, since 693=3*3*7*11 and (2*3^3+7^3+11^3)^(1/3)=1728^(1/3)=12.
MATHEMATICA
criQ[n_]:=IntegerQ[Surd[Total[Flatten[Table[#[[1]], #[[2]]]&/@ FactorInteger[ n]]^3], 3]]; Select[Range[1670000], CompositeQ[#] && criQ[#]&] (* Harvey P. Dale, Sep 19 2021 *)
PROG
(PARI) lista(m) = {for (i=2, m, if (! isprime(i), f = factor(i); s = sum (j=1, length(f~), f[j, 1]^3*f[j, 2]); if (ispower(s, 3), print1(i, ", ")); ); ); } \\ Michel Marcus, Apr 14 2013
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Nov 11 2007
EXTENSIONS
Minor edits by Hieronymus Fischer, Apr 20 2013
STATUS
approved