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

Author

Gage Schacher, Aug 04 2020

Keywords

• base
• nonn
• look

Examples

			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.
		

Links

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

Crossrefs

Cf. A000120 (binary weight), A326889.

Programs

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 *)

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

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).

Extensions

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