A121663 - OEIS

%I #10 Aug 19 2019 20:03:49

%S 1,2,3,6,4,8,12,24,5,10,15,30,20,40,60,120,6,12,18,36,24,48,72,144,30,

%T 60,90,180,120,240,360,720,7,14,21,42,28,56,84,168,35,70,105,210,140,

%U 280,420,840,42,84,126,252,168,336,504,1008,210,420,630,1260,840,1680

%N a(0) = 1; if n = 2^k, a(n) = k+2, otherwise a(n)=(A000523(n)+2)*a(A053645(n)).

%C Each n occurs A045778(n) times in the sequence.

%H Ivan Neretin, <a href="/A121663/b121663.txt">Table of n, a(n) for n = 0..8192</a>

%F G.f.: Product_{k>=0} (1 + (k + 2) * x^(2^k)). - _Ilya Gutkovskiy_, Aug 19 2019

%t f[0] := 1; f[n_] := If[(b = n - 2^(k = Floor[Log2[n]])) == 0, k + 2, (k + 2)*f[b]]; Table[f[n], {n, 0, 61}] (* _Ivan Neretin_, May 09 2015 *)

%o (Scheme:) (define (A121663 n) (cond ((zero? n) 1) ((pow2? n) (+ 2 (A000523 n))) (else (* (+ 2 (A000523 n)) (A121663 (A053645 n))))))

%o (define (pow2? n) (and (> n 0) (zero? (A004198bi n (- n 1)))))

%Y Bisection of A096111.

%K nonn

%O 0,2

%A _Antti Karttunen_, Aug 25 2006