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

1,2

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

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).

Prog

(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))))))

Crossrefs

Cf. A302025 (inverse permutation).

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

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

Sequence in context: A269396 A255408 A269172 * A358373 A285054 A090322

Adjacent sequences: A302023 A302024 A302025 * A302027 A302028 A302029

Keyword

nonn

Author

Antti Karttunen, Apr 03 2018

Status

approved