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Permutation of natural numbers mapping ordinary factorization to "Ludic factorization": a(1) = 1, a(2n) = 2*a(n), a(A003961(n)) = A269379(a(n)).
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%I #12 Apr 06 2018 10:15:15

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,23,20,27,22,25,24,19,26,

%T 21,28,29,30,37,32,39,34,35,36,41,46,63,40,43,54,47,44,33,50,53,48,31,

%U 38,75,52,61,42,65,56,99,58,67,60,71,74,57,64,95,78,77,68,135,70,83,72,89,82,51,92,59,126,91,80,45,86,97,108,155,94,147,88

%N Permutation of natural numbers mapping ordinary factorization to "Ludic factorization": a(1) = 1, a(2n) = 2*a(n), a(A003961(n)) = A269379(a(n)).

%C See comments and examples in A302032 to see how Ludic factorization proceeds.

%H Antti Karttunen, <a href="/A302025/b302025.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

%F a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A269379(a(A064989(2n+1))).

%F a(n) = A269171(A250245(n)).

%F a(n) = A269387(A156552(n)).

%o (PARI)

%o \\ With A269379 precomputed:

%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};

%o A302025(n) = if(1==n,n,if(!(n%2),2*A302025(n/2),A269379(A302025(A064989(n)))));

%o (Scheme, with memoization-macro definec)

%o (definec (A302025 n) (cond ((= 1 n) n) ((even? n) (* 2 (A302025 (/ n 2)))) (else (A269379 (A302025 (A064989 n))))))

%Y Cf. A302026 (inverse permutation).

%Y Cf. A156552, A250245, A269171, A269387 (similar or related permutations).

%Y Cf. A003961, A064989, A269379.

%K nonn

%O 1,2

%A _Antti Karttunen_, Apr 03 2018