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A259942
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Numbers that are larger than or equal to the sum of the cubes of their prime factors (with multiplicity).
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1
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1, 64, 96, 108, 128, 144, 162, 192, 216, 240, 243, 256, 270, 288, 300, 320, 324, 360, 384, 400, 405, 432, 448, 450, 480, 486, 500, 504, 512, 540, 560, 567, 576, 600, 625, 630, 640, 648, 672, 675, 700, 720, 729, 750, 756, 768, 784, 800, 810, 840, 864, 875, 882, 896, 900, 945, 960, 972, 980, 1000
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OFFSET
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1,2
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COMMENTS
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This sequence is analogous to A166319 but with cubes instead of squares.
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LINKS
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EXAMPLE
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64 = 2*2*2*2*2*2 >= 6 * 2^3, so 64 is in the sequence.
96 = 3*2*2*2*2*2 >= 3^3 + 5 * 2^3, so 96 is in the sequence.
256 = 4*4*4*4 >= 4*4^3, so 256 is in the sequence.
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MAPLE
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isA259942 := proc(n)
local ifa;
ifa := ifactors(n)[2] ;
return (n >= add( op(2, p)*op(1, p)^3, p=ifa)) ;
end proc:
for n from 0 to 1000 do
if isA259942(n) then
printf("%d, ", n);
end if;
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MATHEMATICA
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scpfQ[n_]:=n>=Total[Flatten[Table[#[[1]], {#[[2]]}]&/@ FactorInteger[ n]]^3]; Select[Range[1000], scpfQ] (* Harvey P. Dale, Dec 25 2015 *)
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PROG
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(Python)
from sympy import factorint
for j in range(1, 1001):
k = factorint(j)
it = k.keys()
va = k.values()
alfa = 0
for l in range(0, len(k)):
alfa = alfa + va[l]*(it[l]**3)
if alfa <=j:
print j
(PARI) isok(n) = {my(f = factor(n)); n >= sum(k=1, #f~, f[k, 2]*f[k, 1]^3); } \\ Michel Marcus, Nov 28 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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