A349440 a(n) = n / gcd(A001608(n), n), where A001608 = Perrin sequence.

1, 1, 1, 2, 1, 6, 1, 4, 3, 10, 1, 12, 1, 14, 15, 8, 1, 9, 1, 20, 21, 11, 1, 24, 5, 26, 9, 28, 1, 3, 1, 16, 33, 34, 35, 18, 1, 38, 13, 8, 1, 14, 1, 22, 45, 23, 1, 16, 7, 25, 51, 52, 1, 54, 55, 56, 57, 29, 1, 30, 1, 62, 63, 32, 65, 22, 1, 68, 69, 70, 1, 36, 1, 37, 75, 76, 77, 13, 1, 16, 27, 82, 1, 84, 85, 43, 29, 44

Offset

1,4

Comments

The first composite n with a(n) = 1 is n = 521^2 = 271441. See comments in A001608.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(n) = n / A086847(n) = n / gcd(A001608(n), n).

Mathematica

p[1] = 0; p[2] = 2; p[3] = 3; p[n_] := p[n] = p[n - 2] + p[n - 3]; a[n_] := n/GCD[p[n], n]; Array[a, 100] (* Amiram Eldar, Nov 22 2021 *)

Prog

(PARI)
A001608(n) = if(n<0, 0, polsym(x^3-x-1, n)[n+1]); \\ From A001608.
A349440(n) = (n/gcd(n, A001608(n)));

Crossrefs

Cf. A001608, A086847.

Cf. A008578 (subset of the positions of 1's).

Sequence in context: A306927 A277791 A243146 * A048671 A335023 A205959

Adjacent sequences: A349437 A349438 A349439 * A349441 A349442 A349443

Keyword

nonn

Author

Antti Karttunen, Nov 22 2021

Status

approved