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%I #10 Jan 09 2024 10:54:28
%S 1,2,3,1,5,6,7,8,1,10,11,3,13,14,15,16,17,2,19,5,21,22,23,24,1,26,27,
%T 7,29,30,31,32,33,34,35,1,37,38,39,40,41,42,43,11,5,46,47,48,1,2,51,
%U 13,53,54,55,56,57,58,59,15,61,62,7,64,65,66,67,17,69,70
%N The largest unitary divisor of n without an exponent 2 in its prime factorization (A337050).
%H Amiram Eldar, <a href="/A368886/b368886.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^2) = 1, and a(p^e) = p^e if e != 2.
%F a(n) = n / A368884(n).
%F a(n) >= 1, with equality if and only if n is in A062503.
%F a(n) <= n, with equality if and only if n is in A337050.
%F Dirichlet g.f.: zeta(s-1) * Product_{p prime} (1 - 1/p^(2*s-2) + 1/p^(2*s) + 1/p^(3*s-3) - 1/p^(3*s-1)).
%F Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (1 - 1/p^2 + 1/p^3 + 1/p^4 - 1/p^5) = 0.78357388280736936739... .
%t f[p_, e_] := If[e == 2, 1, p^e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i,2] == 2, 1, f[i,1]^f[i,2]));}
%o (Python)
%o from math import prod
%o from sympy import factorint
%o def A368886(n): return prod(p**e for p, e in factorint(n).items() if e!=2) # _Chai Wah Wu_, Jan 09 2024
%Y Cf. A062503, A337050, A368884.
%K nonn,easy,mult
%O 1,2
%A _Amiram Eldar_, Jan 09 2024
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