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A061537 Product of unitary divisors of n.

%I A061537 #31 Jul 22 2024 15:23:16
%S A061537 1,2,3,4,5,36,7,8,9,100,11,144,13,196,225,16,17,324,19,400,441,484,23,
%T A061537 576,25,676,27,784,29,810000,31,32,1089,1156,1225,1296,37,1444,1521,
%U A061537 1600,41,3111696,43,1936,2025,2116,47,2304,49,2500,2601,2704,53,2916
%N A061537 Product of unitary divisors of n.
%C A061537 Also appears to be smallest number m such that A066296(m) = n.
%H A061537 Alois P. Heinz, <a href="/A061537/b061537.txt">Table of n, a(n) for n = 1..20000</a> (terms n=1..1000 from Harry J. Smith)
%F A061537 a(n) = n^(A034444(n)/2) = n^(2^(A001221(n)-1)).
%e A061537 For n = 288, unitary divisors = {1, 9, 32, 288}, a(288) = 1 * 9 * 32 * 288 = 82944.
%p A061537 a:= n-> mul(`if`(igcd(d, n/d)=1, d, 1), d=numtheory[divisors](n)):
%p A061537 seq(a(n), n=1..30);  # _Alois P. Heinz_, Aug 01 2017
%t A061537 Table[Times@@ Select[Divisors[n], GCD[#, n/#]==1 &], {n, 1, 100}] (* _Indranil Ghosh_, Aug 04 2017 *)
%t A061537 a[n_] := n^(2^(PrimeNu[n]-1)); Array[a, 60] (* _Amiram Eldar_, Jul 22 2024 *)
%o A061537 (PARI) { for (n=1, 1000, s=divisors(n); a=1; for (i=2, length(s), d=s[i]; if (gcd(d, n/d)==1, a*=d)); write("b061537.txt", n, " ", a) ) } \\ _Harry J. Smith_, Jul 24 2009
%o A061537 (PARI) a(n) = n^(2^(omega(n)-1)); \\ _Amiram Eldar_, Jul 22 2024
%o A061537 (Python)
%o A061537 from sympy import divisors, gcd, prod
%o A061537 def a(n): return prod(d for d in divisors(n) if gcd(d, n//d)==1)
%o A061537 print([a(n) for n in range(1, 51)]) # _Indranil Ghosh_, Aug 04 2017
%Y A061537 Cf. A000005, A001221, A007955, A007956, A034444, A048105, A066296.
%K A061537 nonn
%O A061537 1,2
%A A061537 _Labos Elemer_, May 15 2001
%E A061537 Corrected and edited by _Jaroslav Krizek_, Mar 05 2009