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A329936
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Binary hoax numbers: composite numbers k such that sum of bits of k equals the sum of bits of the distinct prime divisors of k.
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3
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4, 8, 9, 15, 16, 32, 45, 49, 50, 51, 55, 64, 75, 85, 100, 117, 126, 128, 135, 153, 159, 162, 171, 185, 190, 200, 205, 207, 215, 222, 225, 238, 246, 249, 252, 253, 256, 287, 303, 319, 324, 333, 338, 350, 369, 374, 378, 380, 400, 407, 438, 442, 444, 469, 471
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OFFSET
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1,1
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COMMENTS
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Analogous to A278909 (binary Smith numbers) as A019506 (hoax numbers) is analogous to A006753 (Smith numbers).
Includes all the powers of 2 except for 1 and 2.
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LINKS
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EXAMPLE
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4 = 2^2 is in the sequence since the binary representation of 4 is 100 and 1 + 0 + 0 = 1, and the binary representation of 2 is 10 and 1 + 0 = 1.
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MAPLE
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filter:= proc(n)
if isprime(n) then return false fi;
convert(convert(n, base, 2), `+`) = add(convert(convert(t, base, 2), `+`), t=numtheory:-factorset(n))
end proc:
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MATHEMATICA
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binWt[n_] := Total @ IntegerDigits[n, 2]; binHoaxQ[n_] := CompositeQ[n] && Total[binWt /@ FactorInteger[n][[;; , 1]]] == binWt[n]; Select[Range[500], binHoaxQ]
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PROG
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(PARI) is(n)= my(f=factor(n)[, 1]); sum(i=1, #f, hammingweight(f[i]))==hammingweight(n) && !isprime(n) \\ Charles R Greathouse IV, Nov 28 2019
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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