This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A367513 #11 Nov 23 2023 14:34:00
%S A367513 1,1,1,1,1,1,1,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,8,1,1,27,1,1,1,1,32,1,
%T A367513 1,1,1,1,1,1,8,1,1,1,1,1,1,1,1,1,1,1,1,1,27,1,8,1,1,1,1,1,1,1,64,1,1,
%U A367513 1,1,1,1,1,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A367513 The exponentially evil part of n: the largest unitary divisor of n that is an exponentially evil number (A262675).
%H A367513 Amiram Eldar, <a href="/A367513/b367513.txt">Table of n, a(n) for n = 1..10000</a>
%F A367513 Multiplicative with a(p^e) = p^(e*A010059(e)) = p^A102391(e).
%F A367513 a(n) = n/A367514(n).
%F A367513 A001221(a(n)) = A367512(n).
%F A367513 A034444(a(n)) = A367516(n).
%F A367513 a(n) >= 1, with equality if and only if n is an exponentially odious number (A270428).
%F A367513 a(n) <= n, with equality if and only if n is an exponentially evil number (A262675).
%t A367513 f[p_, e_] := p^(e * (1 - ThueMorse[e])); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A367513 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(hammingweight(f[i, 2])%2, 1, f[i, 1]^f[i, 2]));}
%o A367513 (Python)
%o A367513 from math import prod
%o A367513 from sympy import factorint
%o A367513 def A367513(n): return prod(p**e for p, e in factorint(n).items() if e.bit_count()&1^1) # _Chai Wah Wu_, Nov 23 2023
%Y A367513 Cf. A001969, A010059, A034444, A102391, A262675, A270428, A366902, A366904, A367512, A367516.
%Y A367513 Similar sequences: A350388, A350389, A366906, A367168, A367514.
%K A367513 nonn,easy,mult
%O A367513 1,8
%A A367513 _Amiram Eldar_, Nov 21 2023