cp's OEIS Frontend

A285333 a(n) = A048675(A285332(n)).

%I A285333 #11 Apr 20 2017 09:21:20
%S A285333 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 A285333 16,5,210,16,45,10,35,16,18,5,105,16,28,11,462,28,81,10,21,12,20,7,
%U A285333 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 A285333 a(n) = A048675(A285332(n)).
%C A285333 Following A285332, also this sequence can be represented in a form of a binary tree:
%C A285333                                     0
%C A285333                                     |
%C A285333                  ...................1...................
%C A285333                 2                                       2
%C A285333       3......../ \........4                   4......../ \........3
%C A285333      / \                 / \                 / \                 / \
%C A285333     /   \               /   \               /   \               /   \
%C A285333    /     \             /     \             /     \             /     \
%C A285333   6       4           9       6           5       8           8       4
%C A285333 15 8    12 5        14 10   27 8        10 6    25 12        7 16   16 5
%C A285333 etc.
%H A285333 Antti Karttunen, <a href="/A285333/b285333.txt">Table of n, a(n) for n = 0..1023</a>
%F A285333 a(n) = A048675(A285332(n)).
%F A285333 For all n >= 1, a(2n) = A285332(n).
%F A285333 a(2^n) = A109162(1+n). [The left edge of the tree.]
%F A285333 a(A000225(n)) = n. [The right edge of tree.]
%o A285333 (PARI)
%o A285333 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 A285333 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 A285333 A007947(n) = factorback(factorint(n)[, 1]); \\ From _Andrew Lelechenko_, May 09 2014
%o A285333 A065642(n) = { my(r=A007947(n)); if(1==n,n,n = n+r; while(A007947(n) <> r, n = n+r); n); };
%o A285333 A285332(n) = { if(n<=1,n+1,if(!(n%2),A019565(A285332(n/2)),A065642(A285332((n-1)/2)))); };
%o A285333 A285333(n) = if(!n,n,if(!(n%2),A285332(n/2),A048675(A285332(n))));
%o A285333 (Scheme) (define (A285333 n) (A048675 (A285332 n)))
%Y A285333 Cf. A001477, A048675, A109162, A285325, A285330, A285332 (even bisection).
%K A285333 nonn,tabf
%O A285333 0,3
%A A285333 _Antti Karttunen_, Apr 19 2017