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 A368542 #14 Dec 30 2023 15:21:36
%S A368542 1,1,2,1,1,2,2,1,3,1,1,2,1,2,2,1,1,3,1,1,4,1,1,2,1,1,4,2,1,2,2,1,2,1,
%T A368542 2,3,1,1,2,1,1,4,1,1,3,1,1,2,3,1,2,1,1,4,1,2,2,1,1,2,1,2,6,1,1,2,1,1,
%U A368542 2,2,1,3,1,1,2,1,2,2,1,1,5,1,1,4,1,1,2,1,1,3,2,1,4,1,1,2,1,3,3,1,1,2,1,1,4,1,1,4,1,1,2,2,1,2,1,1,3,1,2,2,1,1,2,2,1,6
%N A368542 The number of divisors of n whose prime factors are all Mersenne primes (A000668).
%C A368542 The number of terms of A056652 U {1} that divide n.
%H A368542 Amiram Eldar, <a href="/A368542/b368542.txt">Table of n, a(n) for n = 1..10000</a>
%F A368542 Multiplicative with a(p^e) = e+1 if p is a Mersenne prime (A000668), and 1 otherwise.
%F A368542 a(n) >= 1, with equality if and only if n is in A161790.
%F A368542 a(n) <= A000005(n), with equality if and only if n is in A056652 U {1}.
%F A368542 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/Product_{k>=1} (1 - 1/A000668(k)) = 1.82292512097260346512... .
%t A368542 q[n_] := AllTrue[FactorInteger[n][[;; , 1]], # + 1 == 2^IntegerExponent[# + 1, 2] &]; f[p_, e_] := If[q[p], e + 1, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A368542 (PARI) a(n) = {my(f=factor(n)); prod(i=1, #f~, if((f[i,1]+1) >> valuation(f[i,1]+1, 2) == 1 , f[i,2] + 1, 1))};
%Y A368542 Cf. A000005, A000668, A056652, A161790.
%K A368542 nonn,easy,mult
%O A368542 1,3
%A A368542 _Amiram Eldar_, Dec 29 2023