%I #14 Nov 10 2023 12:27:08
%S 1,2,3,4,5,6,7,1,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,3,25,26,
%T 1,28,29,30,31,1,33,34,35,36,37,38,39,5,41,42,43,44,45,46,47,48,49,50,
%U 51,52,53,2,55,7,57,58,59,60,61,62,63,1,65,66,67,68,69,70
%N The largest unitary divisor of n that is a term of A138302.
%C First differs from A056192 at n = 32 and from A270418 at n = 128.
%H Amiram Eldar, <a href="/A367168/b367168.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = p^A048298(e).
%F a(n) <= n, with equality if and only if n is in A138302.
%F Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 0.881513... (A065465).
%t f[p_, e_] := If[e == 2^IntegerExponent[e, 2], p^e, 1]; 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] == 1 << valuation(f[i, 2], 2), f[i, 1]^f[i, 2], 1));}
%o (Python)
%o from math import prod
%o from sympy import factorint
%o def A367168(n): return prod(p**e for p,e in factorint(n).items() if not(e&-e)^e) # _Chai Wah Wu_, Nov 10 2023
%Y Cf. A048298, A065465, A138302, A367169, A367170, A367171.
%Y Cf. A056192, A270418.
%Y Similar sequences: A350388, A350389, A360539.
%K nonn,easy,mult
%O 1,2
%A _Amiram Eldar_, Nov 07 2023