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

%I A292269 #14 Jan 30 2025 05:09:04
%S A292269 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,
%T A292269 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,
%U A292269 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
%N A292269 If n is 1 or a prime, then a(n) = 1, otherwise a(n) = the third smallest divisor of n.
%H A292269 Antti Karttunen, <a href="/A292269/b292269.txt">Table of n, a(n) for n = 1..10000</a>
%F A292269 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).
%t A292269 a[n_?PrimeQ] = 1; a[1] = 1; a[n_] := Divisors[n][[3]]; Array[a, 100] (* _Amiram Eldar_, Jan 30 2025 *)
%o A292269 (PARI) A292269(n) = { my(ds=divisors(n)); if(numdiv(n)<3,1,ds[3]); }
%o A292269 (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)))
%Y A292269 Cf. A000005, A020639, A119288, A171783, A283050, A284255, A284260.
%Y A292269 Cf. A008578 (positions of ones).
%K A292269 nonn
%O A292269 1,4
%A A292269 _Antti Karttunen_, Oct 04 2017