A323506 - OEIS

%I #12 Jan 17 2019 17:20:01

%S 1,2,4,3,8,12,6,4,16,24,24,24,12,18,8,5,32,48,48,48,48,72,48,40,24,36,

%T 36,36,16,24,10,6,64,96,96,96,96,144,96,80,96,144,144,144,96,144,80,

%U 60,48,72,72,72,72,108,72,60,32,48,48,48,20,30,12,7,128,192,192,192,192,288,192,160,192,288,288,288,192,288,160,120

%N a(n) = A323505(n) / A246660(n).

%H Antti Karttunen, <a href="/A323506/b323506.txt">Table of n, a(n) for n = 0..16383</a>

%F a(n) = A323505(n) / A246660(n).

%F For n > 1, a(2n) = 2*a(n).

%e This sequence can be represented as a binary tree, as both A323505 and A246660 have similar tree structures:

%e                                        1

%e                                        |

%e                     ...................2....................

%e                    4                                        3

%e          8......../ \........12                  6........./ \.......4

%e         / \                 / \                 / \                 / \

%e        /   \               /   \               /   \               /   \

%e       /     \             /     \             /     \             /     \

%e     16       24         24       24         12       18          8       5

%e   32  48   48  48     48  72   48  40     24  36   36  36      16 24   10  6

%e etc.

%o (PARI)

%o A001511(n) = (1+valuation(n,2));

%o A036987(n) = !bitand(n,1+n);

%o A323505(n) = if(!n,1,if(!(n%2), 2*A323505(n/2), (A001511(n+1)+1-A036987(n))*A323505((n-1)/2)));

%o A246660(n) = { my(i=0, p=1); while(n>0, if(n%2, i++; p = p * i, i = 0); n = n\2); p; };

%o A323506(n) = (A323505(n)/A246660(n));

%Y Cf. A246660, A323505.

%K nonn

%O 0,2

%A _Antti Karttunen_, Jan 16 2019