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 A382941 #17 Apr 29 2025 16:52:45
%S A382941 1,2,3,2,5,1,7,4,3,1,11,3,13,1,1,16,17,2,19,5,1,1,23,18,5,1,9,7,29,1,
%T A382941 31,64,1,1,1,36,37,1,1,50,41,1,43,11,5,1,47,72,7,2,1,13,53,12,1,98,1,
%U A382941 1,59,15,61,1,7,512,1,1,67,17,1,1,71,648,73,1,3,19
%N A382941 a(n) = exp(Sum_{d|n} A382883(d)*log(n/d)).
%C A382941 See the comments in A382883.
%F A382941 Restricting the sum to prime divisors of n gives A205959(n).
%F A382941 a(k) = 1 <=> k in A000469 <=> k is a nonprime squarefree number.
%F A382941 a(k) != 1 <=> k in A383263 <=> k is prime or divisible by a square greater than 1.
%p A382941 h := proc(n) option remember; local j; ifelse(n = 1, 1,
%p A382941 -add(ifelse(j = 1, 1, padic:-ordp(n, j))*h(j), j = 1..n-1)) end:
%p A382941 a := n -> local d; simplify(exp(add(h(d)*log(n/d), d in numtheory:-divisors(n)))):
%p A382941 seq(a(n), n = 1..76);
%t A382941 V[n_, e_] := If[e == 1, 1, IntegerExponent[n, e]]; f[n_] := f[n] = -DivisorSum[n, V[n, #] * f[#] &, # < n &]; f[1] = 1; a[n_] := Exp[DivisorSum[n, f[#] * Log[n/#] &]]; Array[a, 100] (* _Amiram Eldar_, Apr 29 2025 *)
%o A382941 (SageMath)
%o A382941 def A382941(n: int) -> int: return simplify(exp(sum(A382883(d)*log(n//d) for d in n.divisors())))
%o A382941 print([A382941(n) for n in srange(1, 76)]);
%Y A382941 Cf. A000469, A014963, A205959, A382883, A383263.
%K A382941 nonn
%O A382941 1,2
%A A382941 _Peter Luschny_, Apr 09 2025