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%I #12 Mar 06 2019 08:36:46
%S 1,2,6,4,10,6,42,8,18,10,66,12,156,42,60,16,34,18,228,20,42,66,92,24,
%T 300,156,108,84,116,60,310,32,66,34,420,36,222,228,156,40,246,42,172,
%U 132,180,92,2820,48,588,300,204,156,212,108,660,168,228,116,590,60
%N a(n) is the least positive multiple of n belonging to A306263 if any, or a(n) = -1 otherwise.
%C Is a(n) > 0 for every n > 0?
%F a(A306263(n)) = A306263(n) for any n > 0.
%e For n = 7:
%e - the divisors of 7 are: 1, 7,
%e - the corresponding Hamming weights are: 1, 3,
%e - 3 does not divide 7,
%e - the divisors of 3*7 are: 1, 3, 7, 21,
%e - the corresponding Hamming weights are: 1, 2, 3, 3,
%e - 2 does not divide 3*7,
%e - the divisors of 2*3*7 are: 1, 2, 3, 6, 7, 14, 21, 42,
%e - the corresponding Hamming weights are: 1, 1, 2, 2, 3, 3, 3, 3,
%e - they all divide 2*3*7,
%e - hence a(7) = 2*3*7 = 42.
%t With[{s = Select[Range[3000], With[{k = #}, AllTrue[Divisors@ k, Mod[k, DigitCount[#, 2, 1]] == 0 &]] &]}, Table[SelectFirst[s, Mod[#, n] == 0 &] /. k_ /; MissingQ@ k -> -1, {n, 60}]] (* _Michael De Vlieger_, Mar 05 2019 *)
%o (PARI) a(n) = while (1, my (m=n); fordiv (m, d, m = lcm(m, hammingweight(d));); if (n==m, return (n), n = m))
%Y Cf. A000120, A306263.
%K nonn,base
%O 1,2
%A _Rémy Sigrist_, Mar 03 2019
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