A336823 a(1)=1; thereafter a(n) = a(n-1) / wt(n-1) if wt(n-1) divides a(n-1), otherwise a(n) = a(n-1) * wt(n-1) where wt(n) is the binary weight of n.

1, 1, 1, 2, 2, 1, 2, 6, 6, 3, 6, 2, 1, 3, 1, 4, 4, 2, 1, 3, 6, 2, 6, 24, 12, 4, 12, 3, 1, 4, 1, 5, 5, 10, 5, 15, 30, 10, 30, 120, 60, 20, 60, 15, 5, 20, 5, 1, 2, 6, 2, 8, 24, 6, 24, 120, 40, 10, 40, 8, 2, 10, 2, 12, 12, 6, 3, 1, 2, 6, 2, 8, 4, 12, 4, 1, 3, 12

Offset

1,4

Links

Gage Schacher, Table of n, a(n) for n = 1..10000

Formula

a(n) = a(n-1)/A000120(n-1) iff A000120(n-1) is a factor of a(n-1), otherwise a(n) = a(n-1)*A000120(n-1).

Example

a(1)=1 is given, and has 1, the binary weight of 1, as a factor so a(2) =1/1=1;
a(2)=1 which has 1, the binary weight of 2, as a factor so a(3) =1/1=1;
a(3)=1 which does not have 2, the binary weight of 3, as a factor so a(4) =1*2=2.

Mathematica

a[1] = 1; a[n_] := a[n] = If[Divisible[a[n-1], (w = DigitCount[n-1, 2, 1])], a[n-1] / w, a[n-1] * w]; Array[a, 100] (* Amiram Eldar, Aug 05 2020 *)

Prog

(PARI) a(n) = if (n==1, 1, my(h=hammingweight(n-1), last=a(n-1)); if (last%h, last*h, last/h)); \\ Michel Marcus, Aug 05 2020

Crossrefs

Cf. A000120 (binary weight), A326889.

Sequence in context: A335190 A283170 A368836 * A375062 A236144 A226328

Adjacent sequences: A336820 A336821 A336822 * A336824 A336825 A336826

Keyword

base,nonn,look

Author

Gage Schacher, Aug 04 2020

Extensions

a(1)=1 added to definition. - N. J. A. Sloane, Sep 21 2020

Status

approved