A306645 a(n) is the least positive multiple of n belonging to A306263 if any, or a(n) = -1 otherwise.

1, 2, 6, 4, 10, 6, 42, 8, 18, 10, 66, 12, 156, 42, 60, 16, 34, 18, 228, 20, 42, 66, 92, 24, 300, 156, 108, 84, 116, 60, 310, 32, 66, 34, 420, 36, 222, 228, 156, 40, 246, 42, 172, 132, 180, 92, 2820, 48, 588, 300, 204, 156, 212, 108, 660, 168, 228, 116, 590, 60

Offset: 1

Author

Rémy Sigrist, Mar 03 2019

Keywords

• nonn
• base

Comments

Is a(n) > 0 for every n > 0?

Examples

			For n = 7:
- the divisors of 7 are: 1, 7,
- the corresponding Hamming weights are: 1, 3,
- 3 does not divide 7,
- the divisors of 3*7 are: 1, 3, 7, 21,
- the corresponding Hamming weights are: 1, 2, 3, 3,
- 2 does not divide 3*7,
- the divisors of 2*3*7 are: 1, 2, 3, 6, 7, 14, 21, 42,
- the corresponding Hamming weights are: 1, 1, 2, 2, 3, 3, 3, 3,
- they all divide 2*3*7,
- hence a(7) = 2*3*7 = 42.
		

Crossrefs

Cf. A000120, A306263.

Programs

Mathematica

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 *)

PARI

a(n) = while (1, my (m=n); fordiv (m, d, m = lcm(m, hammingweight(d));); if (n==m, return (n), n = m))

Formula

a(A306263(n)) = A306263(n) for any n > 0.