A243352 If n is k-th squarefree number [i.e., n = A005117(k)], a(n) = 2k-1; otherwise, when n is k-th nonsquarefree number [i.e., n = A013929(k)], a(n) = 2k.

1, 3, 5, 2, 7, 9, 11, 4, 6, 13, 15, 8, 17, 19, 21, 10, 23, 12, 25, 14, 27, 29, 31, 16, 18, 33, 20, 22, 35, 37, 39, 24, 41, 43, 45, 26, 47, 49, 51, 28, 53, 55, 57, 30, 32, 59, 61, 34, 36, 38, 63, 40, 65, 42, 67, 44, 69, 71, 73, 46, 75, 77, 48, 50, 79, 81, 83, 52, 85, 87, 89

Offset: 1

Author

Antti Karttunen, Jun 04 2014

Keywords

• nonn
• easy

Comments

Odd numbers occur (in order) at the positions given by squarefree numbers, A005117, and even numbers occur (in order) at the positions given by their complement, nonsquarefree numbers, A013929.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A088610. Cf. A243343, A072062.

Programs

Scheme

(define (A243352 n) (if (zero? (A008966 n)) (* 2 (A057627 n)) (+ (* 2 (A013928 n)) 1)))

Formula

If mu(n) = 0, a(n) = 2*A057627(n), otherwise, a(n) = 1 + 2 * A013928(n). [Here mu is Moebius mu-function, A008683, which is zero only when n is a nonsquarefree number, one of the numbers in A013929].

For all n, A000035(a(n)) = A008966(n) = A008683(n)^2, or equally, a(n) = mu(n) modulo 2.