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%I #13 Jul 07 2019 13:09:07
%S 1,4,9,16,25,36,49,512,81,100,121,144,169,196,225,65536,289,324,361,
%T 400,441,484,529,4608,625,676,19683,784,841,900,961,33554432,1089,
%U 1156,1225,1296,1369,1444,1521,12800,1681,1764,1849,1936,2025,2116,2209,589824
%N Multiplicative with a(p) = p^2 and a(p^e) = p^a(e) for any e > 1 and prime number p.
%C To compute a(n): square every prime number at leaf position in the prime tower factorization of n (the prime tower factorization of a number is defined in A182318).
%C For any n > 0, a(n) is the least k such that A308993(k) = n.
%H Rémy Sigrist, <a href="/A309002/b309002.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A309002/a309002.pdf">Illustration of first terms</a>
%F A308993(a(n)) = n.
%F A185102(a(n)) = 1 + A185102(n) for any n > 1.
%F a(n) >= n^2 with equality iff n is cubefree (A004709).
%e See Links section.
%o (PARI) a(n) = my (f=factor(n)); prod (i=1, #f~, f[i, 1]^if (f[i, 2]==1, 2, a(f[i, 2])))
%Y Cf. A004709, A182318, A185102, A308993.
%K nonn,mult
%O 1,2
%A _Rémy Sigrist_, Jul 05 2019
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