

A329936


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.


3



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

1,1


COMMENTS

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.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000


EXAMPLE

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.


MAPLE

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:
select(filter, [$2..1000]); # Robert Israel, Nov 28 2019


MATHEMATICA

binWt[n_] := Total @ IntegerDigits[n, 2]; binHoaxQ[n_] := CompositeQ[n] && Total[binWt /@ FactorInteger[n][[;; , 1]]] == binWt[n]; Select[Range[500], binHoaxQ]


PROG

(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


CROSSREFS

Cf. A006753, A019506, A278909.
Sequence in context: A078177 A326692 A336663 * A023886 A158337 A161542
Adjacent sequences: A329933 A329934 A329935 * A329937 A329938 A329939


KEYWORD

nonn,base


AUTHOR

Amiram Eldar, Nov 24 2019


STATUS

approved



