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%I #26 Jul 14 2020 22:56:28
%S 1,1,2,2,6,3,30,4,3,5,210,8,2310,7,10,4,30030,9,510510,24,14,11,
%T 9699690,12,5,13,18,120,223092870,15,6469693230,16,22,17,42,6,
%U 200560490130,19,26,20,7420738134810,21,304250263527210,840,54,23,13082761331670030,32,7,25,34,9240,614889782588491410,27,66,28,38,29
%N If n is a square, a(n) = A000196(n), and for nonsquare n, let p be the smallest prime dividing the squarefree part of n. Divide n by p and multiply by the product of all smaller primes.
%C Each natural numbers occurs exactly twice in this sequence.
%C In binary trees like A334860 and A334866, for n > 2, a(n) gives the parent node of node n.
%C For nonsquare numbers, n, with squarefree part A019565(k) and square part m, a(n) is the number with squarefree part A019565(k-1) and square part m. - _Peter Munn_, Jul 14 2020
%H Antti Karttunen, <a href="/A334870/b334870.txt">Table of n, a(n) for n = 1..1024</a>
%F a(A334747(n)) = n.
%F a(A000040(n)) = A002110(n-1).
%F a(n^2) = n.
%F a(n) = A225546(A252463(A225546(n))). - _Peter Munn_, Jun 08 2020
%t Array[If[IntegerQ[#2], #2, #1/#2*Product[Prime@i, {i, PrimePi@#2 - 1}] & @@ {#1, FactorInteger[#2 /. (c_ : 1)*a_^(b_ : 0) :> (c*a^b)^2][[1, 1]]}] & @@ {#, Sqrt[#]} &, 58] (* _Michael De Vlieger_, Jun 26 2020 *)
%o (PARI) A334870(n) = if(issquare(n),sqrtint(n),my(c=core(n), m=n); forprime(p=2, , if(!(c % p), m/=p; break, m*=p)); (m));
%Y A left inverse of A334747.
%Y Cf. A000196, A019565, A225546, A252463, A334860, A334866, A334868, A334869, A334871, A334872.
%K nonn
%O 1,3
%A _Antti Karttunen_, Jun 08 2020
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