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A122733
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Least sum of n positive cubes to have exactly n prime factors, with multiplicity.
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1
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9, 66, 56, 108, 144, 192, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| Sequence begins with n = 2 because a(1) is undefined (sum of one positive cube cannot have exactly one prime factor, i.e. be prime).
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FORMULA
| a(n) = Min{x = (c_1)^3 + (c_2)^3 + ... + (c_n)^3 such that omega(x) = A001222(x) = n}.
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EXAMPLE
| a(2) = least semiprime in A003325 = 9 = 3 * 3 = 1^3 + 2^3 = A085366(1).
a(3) = least 3-almost prime in A003072 = 66 = 2 * 3 * 11 = 1^3 + 1^3 + 4^3 = A003072(10).
a(4) = least 4-almost prime in A003327 = 56 = 2^3 * 7 = 1^3 + 1^3 + 3^3 + 3^3 = A003327(10).
a(5) = least 5-almost prime in A003328 = 108 = 2^2 * 3^3 = 4^3 + 3^3 + 2^3 + 2^3 + 1^3 = A003328(25).
a(6) = least 6-almost prime in A003329 = 144 = 2^4 * 3^2 = 5^3 + 2^3 + 2^3 + 1^3 + 1^3 + 1^3 = A003329(46).
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MAPLE
| isSumcPosC := proc(n, c, minb)
local nrt ;
if c = 1 then nrt := iroot(n, 3) ; if nrt^3 = n and n>= minb then true; else false; end if;
else for b from minb do if b^3 > n then return false; end if; if isSumcPosC(n-b^3, c-1, b) then return true; end if; end do: end if;
end proc:
A122733 := proc(n)
for a from 1 do if numtheory[bigomega](a) = n then if isSumcPosC(a, n, 1) then return a; end if; end if;
end do:
end proc:
for n from 2 do print(A122733(n)) ; end do: # R. J. Mathar, Dec 22 2010
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CROSSREFS
| Cf. A000578, A001222, A003072, A003325, A003327, A003328, A003329, A085366.
Sequence in context: A100311 A120286 A152581 * A118465 A051375 A081902
Adjacent sequences: A122730 A122731 A122732 * A122734 A122735 A122736
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 23 2006
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