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%I #12 Apr 06 2018 10:15:22
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,25,20,27,22,19,24,23,26,
%T 21,28,29,30,49,32,45,34,35,36,31,50,33,40,37,54,41,44,81,38,43,48,
%U 125,46,75,52,47,42,121,56,63,58,77,60,53,98,39,64,55,90,59,68,135,70,61,72,169,62,51,100,67,66,175,80,99,74,71,108,343,82,105,88
%N Permutation of natural numbers mapping "Ludic factorization" to ordinary factorization: a(1) = 1, a(2n) = 2*a(n), a(A269379(n)) = A003961(a(n)).
%C See comments and examples in A302032 to see how Ludic factorization proceeds.
%H Antti Karttunen, <a href="/A302026/b302026.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) = A003961(a(A269380(2n+1))).
%F a(n) = A250246(A269172(n)).
%F a(n) = A005940(1+A269388(n)).
%F Other identities. For all n >= 1:
%F A001221(a(n)) = A302031(n).
%F A001222(a(n)) = A302037(n).
%o (PARI)
%o \\ With A269380 precomputed:
%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A302026(n) = if(1==n,n,if(!(n%2),2*A302026(n/2),A003961(A302026(A269380(n)))));
%o (Scheme, with memoization-macro definec)
%o (definec (A302026 n) (cond ((= 1 n) n) ((even? n) (* 2 (A302026 (/ n 2)))) (else (A003961 (A302026 (A269380 n))))))
%Y Cf. A302025 (inverse permutation).
%Y Cf. A005940, A250246, A269172, A269388 (similar or related permutations).
%Y Cf. A003961, A064989, A269379, A269380, A302031, A302032, A302034, A302037.
%K nonn
%O 1,2
%A _Antti Karttunen_, Apr 03 2018
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