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 A306263 Numbers k such that, for any divisor d of k, the Hamming weight of d divides k. 3
 1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 32, 34, 36, 40, 42, 48, 60, 64, 66, 68, 72, 80, 84, 92, 96, 108, 116, 120, 126, 128, 132, 136, 144, 156, 160, 168, 172, 180, 184, 192, 204, 212, 216, 222, 228, 232, 240, 246, 252, 256, 264, 272, 276, 284, 288, 300, 310 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Hamming weight of a number is given by A000120. This sequence is a binary variant of A285815. This sequence is infinite as it contains all powers of 2 (A000079). All terms belong to A049445. If k belongs to the sequence, then 2*k belongs to the sequence. All terms except 1 are even. - Robert Israel, Mar 05 2019 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE For n = 108: - the divisors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, - the corresponding Hamming weights are 1, 1, 2, 1, 2, 2, 2, 2, 4, 2, 4, 4, - they all divide 108, - hence 108 belongs to the sequence. For n = 98: - the divisors of 98 are 1, 2, 7, 14, 49, 98, - the correspond Hamming weights are 1, 1, 3, 3, 3, 3, - 3 does not divide 98, - hence 98 does not belong to the sequence. MAPLE filter:= proc(n) local F; F:= map(convert, map(convert, numtheory:-divisors(n), base, 2), `+`); andmap(t -> n mod t = 0, F) end proc: select(filter, [\$1..1000]); # Robert Israel, Mar 05 2019 MATHEMATICA Select[Range@ 310, With[{k = #}, AllTrue[Divisors@ k, Mod[k, DigitCount[#, 2, 1]] == 0 &]] &] (* Michael De Vlieger, Mar 05 2019 *) PROG (PARI) is(n) = fordiv(n, d, if (n%hammingweight(d), return (0))); return ( ) (Magma) [k:k in [1..310]| forall{d:d in Divisors(k)| k mod &+Intseq(d, 2) eq 0}]; // Marius A. Burtea, Dec 30 2019 CROSSREFS Cf. A000079, A000120, A049445, A141586, A285815. Positions of zeros in A324393. Sequence in context: A267817 A177917 A071594 * A071596 A090778 A097380 Adjacent sequences: A306260 A306261 A306262 * A306264 A306265 A306266 KEYWORD nonn,base AUTHOR Rémy Sigrist, Mar 02 2019 STATUS approved

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Last modified October 3 17:45 EDT 2023. Contains 365870 sequences. (Running on oeis4.)