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.

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

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: A326692 A373375 A336663 * A023886 A158337 A161542

Adjacent sequences: A329933 A329934 A329935 * A329937 A329938 A329939

Keyword

nonn,base

Author

Amiram Eldar, Nov 24 2019

Status

approved