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

Author

Antti Karttunen, Oct 04 2017

Keywords

• nonn

Links

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

Crossrefs

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

Cf. A008578 (positions of ones).

Programs

Mathematica

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

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)))

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).