A302026 Permutation of natural numbers mapping "Ludic factorization" to ordinary factorization: a(1) = 1, a(2n) = 2*a(n), a(A269379(n)) = A003961(a(n)).

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, 21, 28, 29, 30, 49, 32, 45, 34, 35, 36, 31, 50, 33, 40, 37, 54, 41, 44, 81, 38, 43, 48, 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

Offset: 1

Author

Antti Karttunen, Apr 03 2018

Keywords

• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences generated by sieves

Crossrefs

Cf. A302025 (inverse permutation).

Cf. A005940, A250246, A269172, A269388 (similar or related permutations).

Cf. A003961, A064989, A269379, A269380, A302031, A302032, A302034, A302037.

Programs

PARI

\\ With A269380 precomputed:
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A302026(n) = if(1==n,n,if(!(n%2),2*A302026(n/2),A003961(A302026(A269380(n)))));
(Scheme, with memoization-macro definec)
(definec (A302026 n) (cond ((= 1 n) n) ((even? n) (* 2 (A302026 (/ n 2)))) (else (A003961 (A302026 (A269380 n))))))

Formula

a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A003961(a(A269380(2n+1))).

a(n) = A250246(A269172(n)).

a(n) = A005940(1+A269388(n)).

Other identities. For all n >= 1:

A001221(a(n)) = A302031(n).

A001222(a(n)) = A302037(n).