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 A370077 #7 Feb 11 2024 05:08:00
%S A370077 1,1,1,2,1,1,1,1,2,1,1,2,1,1,1,4,1,2,1,2,1,1,1,1,2,1,1,2,1,1,1,1,1,1,
%T A370077 1,4,1,1,1,1,1,1,1,2,2,1,1,4,2,2,1,2,1,1,1,1,1,1,1,2,1,1,2,1,1,1,1,2,
%U A370077 1,1,1,2,1,1,2,2,1,1,1,4,4,1,1,2,1,1,1
%N A370077 The product of exponents of the prime factorization of the largest unitary divisor of n that is a term of A138302.
%H A370077 Amiram Eldar, <a href="/A370077/b370077.txt">Table of n, a(n) for n = 1..10000</a>
%F A370077 a(n) = A005361(A367168(n)).
%F A370077 a(n) = A006519(A005361(n)).
%F A370077 a(n) = 2^A370078(n).
%F A370077 a(n) = 1 if and only if n is an exponentially odd number (A268335).
%F A370077 a(n) <= A005361(n), with equality if and only if n is an exponentially 2^n-number (A138302).
%F A370077 Multiplicative with a(p^e) = e if e is a power of 2, and 1 otherwise.
%F A370077 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + Sum_{k>=1} (2^k-1)*(1/p^(2^k) - 1/p^(2^k+1))) = 1.47219167074464124662... .
%t A370077 f[p_, e_] := If[e == 2^IntegerExponent[e, 2], e, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A370077 (PARI) ispow2(n) = n >> valuation(n, 2) == 1;
%o A370077 a(n) = vecprod(apply(x -> if(ispow2(x), x, 1), factor(n)[, 2]));
%Y A370077 Cf. A005361, A006519, A138302, A268335, A367168, A370078.
%K A370077 nonn,easy,mult
%O A370077 1,4
%A A370077 _Amiram Eldar_, Feb 09 2024