A133923 a(1)=1, and for n>1, a(n) = a(n-1)/2, if a(n-1) is divisible by 2, otherwise a(n) = A000005(n*a(n-1)).

1, 2, 1, 3, 4, 2, 1, 4, 2, 1, 2, 1, 2, 1, 4, 2, 1, 6, 3, 12, 6, 3, 4, 2, 1, 4, 2, 1, 2, 1, 2, 1, 4, 2, 1, 9, 6, 3, 6, 3, 4, 2, 1, 6, 3, 8, 4, 2, 1, 6, 3, 12, 6, 3, 8, 4, 2, 1, 2, 1, 2, 1, 6, 3, 8, 4, 2, 1, 4, 2, 1, 12, 6, 3, 9, 18, 9, 16, 8, 4, 2, 1, 2, 1, 4, 2, 1, 8, 4, 2, 1, 6, 3, 8, 4, 2, 1, 6, 3, 18

Offset

1,2

Comments

The formula could be generalized to a class of sequences as a(n)= A000005(A*a(n-1)+B) if a(n-1) is not divisible by C, else a(n)= a(n-1)/C, where A, B, C are integers. In this case we have A=n, B=0 and C=2.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

nxt[{n_, a_}]:={n+1, If[Mod[a, 2]==0, a/2, DivisorSigma[0, a(n+1)]]}; NestList[nxt, {1, 1}, 100][[;; , 2]] (* Harvey P. Dale, Oct 28 2025 *)

Prog

(Scheme) (define (A133923 n) (cond ((< n 2) n) ((even? (A133923 (-1+ n))) (/ (A133923 (-1+ n)) 2)) (else (A000005 (* n (A133923 (-1+ n)))))))

Crossrefs

Cf. A000005.

Sequence in context: A286539 A004741 A352840 * A347296 A341231 A379004

Adjacent sequences: A133920 A133921 A133922 * A133924 A133925 A133926

Keyword

nonn

Author

Ctibor O. Zizka, Jan 07 2008

Extensions

Edited, corrected, extended and Scheme-code added by Antti Karttunen, Oct 05 2009

Status

approved