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A349440
a(n) = n / gcd(A001608(n), n), where A001608 = Perrin sequence.
1
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
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. A008578 (subset of the positions of 1's).
Sequence in context: A306927 A277791 A243146 * A048671 A335023 A205959
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 22 2021
STATUS
approved