A292269 If n is 1 or a prime, then a(n) = 1, otherwise a(n) = the third smallest divisor of n.

1, 1, 1, 4, 1, 3, 1, 4, 9, 5, 1, 3, 1, 7, 5, 4, 1, 3, 1, 4, 7, 11, 1, 3, 25, 13, 9, 4, 1, 3, 1, 4, 11, 17, 7, 3, 1, 19, 13, 4, 1, 3, 1, 4, 5, 23, 1, 3, 49, 5, 17, 4, 1, 3, 11, 4, 19, 29, 1, 3, 1, 31, 7, 4, 13, 3, 1, 4, 23, 5, 1, 3, 1, 37, 5, 4, 11, 3, 1, 4, 9, 41, 1, 3, 17, 43, 29, 4, 1, 3, 13, 4, 31, 47, 19, 3, 1, 7, 9, 4, 1, 3, 1, 4, 5

Offset

1,4

Links

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

Formula

If A020639(n)^2 divides n [when n is in A283050] and either A119288(n) = 1 or A020639(n)^2 < A119288(n), then a(n) = A020639(n)^2, otherwise a(n) = A119288(n).

Mathematica

a[n_?PrimeQ] = 1; a[1] = 1; a[n_] := Divisors[n][[3]]; Array[a, 100] (* Amiram Eldar, Jan 30 2025 *)

Prog

(PARI) A292269(n) = { my(ds=divisors(n)); if(numdiv(n)<3, 1, ds[3]); }
(Scheme) (define (A292269 n) (let ((x (A000290 (A020639 n))) (y (A119288 n))) (if (and (zero? (modulo n x)) (or (= 1 y) (< x y))) x y)))

Crossrefs

Cf. A000005, A020639, A119288, A171783, A283050, A284255, A284260.

Cf. A008578 (positions of ones).

Sequence in context: A232633 A089612 A353776 * A010127 A263022 A326690

Adjacent sequences: A292266 A292267 A292268 * A292270 A292271 A292272

Keyword

nonn

Author

Antti Karttunen, Oct 04 2017

Status

approved