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a(n) = A048675(A285332(n)).
7

%I #11 Apr 20 2017 09:21:20

%S 0,1,2,2,3,4,4,3,6,4,9,6,5,8,8,4,15,8,12,5,14,10,27,8,10,6,25,12,7,16,

%T 16,5,210,16,45,10,35,16,18,5,105,16,28,11,462,28,81,10,21,12,20,7,

%U 154,26,125,16,30,8,49,24,11,32,32,6,10659,212,420,17,910,46,75,10,78,36,175,20,33,20,24,6,3094,106,315,18,385,32,56,17,780045

%N a(n) = A048675(A285332(n)).

%C Following A285332, also this sequence can be represented in a form of a binary tree:

%C 0

%C |

%C ...................1...................

%C 2 2

%C 3......../ \........4 4......../ \........3

%C / \ / \ / \ / \

%C / \ / \ / \ / \

%C / \ / \ / \ / \

%C 6 4 9 6 5 8 8 4

%C 15 8 12 5 14 10 27 8 10 6 25 12 7 16 16 5

%C etc.

%H Antti Karttunen, <a href="/A285333/b285333.txt">Table of n, a(n) for n = 0..1023</a>

%F a(n) = A048675(A285332(n)).

%F For all n >= 1, a(2n) = A285332(n).

%F a(2^n) = A109162(1+n). [The left edge of the tree.]

%F a(A000225(n)) = n. [The right edge of tree.]

%o (PARI)

%o A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from _M. F. Hasler_

%o A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ _Michel Marcus_, Oct 10 2016

%o A007947(n) = factorback(factorint(n)[, 1]); \\ From _Andrew Lelechenko_, May 09 2014

%o A065642(n) = { my(r=A007947(n)); if(1==n,n,n = n+r; while(A007947(n) <> r, n = n+r); n); };

%o A285332(n) = { if(n<=1,n+1,if(!(n%2),A019565(A285332(n/2)),A065642(A285332((n-1)/2)))); };

%o A285333(n) = if(!n,n,if(!(n%2),A285332(n/2),A048675(A285332(n))));

%o (Scheme) (define (A285333 n) (A048675 (A285332 n)))

%Y Cf. A001477, A048675, A109162, A285325, A285330, A285332 (even bisection).

%K nonn,tabf

%O 0,3

%A _Antti Karttunen_, Apr 19 2017