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 A064084 #11 Aug 31 2023 05:29:41
%S A064084 1,3,7,15,31,21,127,255,511,93,2047,105,8191,381,217,65535,131071,
%T A064084 1533,524287,465,889,6141,8388607,1785,33554431,24573,134217727,1905,
%U A064084 536870911,651,2147483647,4294967295,14329,393213,3937,7665,137438953471,1572861,57337
%N A064084 A multiplicative version of 2^n - 1 (A000225).
%C A064084 Since n -> 2^n - 1 is an embedding of the ordered structure N = {1, 2, 3, ...} (the order being the "divides" relation) into itself, a(n) always divides A000225(n); the sequence of quotients of A000225 and a is A064085.
%H A064084 Alois P. Heinz, <a href="/A064084/b064084.txt">Table of n, a(n) for n = 1..1000</a>
%F A064084 a(n) = (2^((p_1)^(e_1)) - 1) * ... * (2^((p_k)^(e_k)) - 1) where (p_1)^(e_1) * ... * (p_k)^(e_k) is the prime factorization of n.
%e A064084 a(6) = (2^2 - 1) * (2^3 - 1) = 21 since 6 = 2 * 3.
%p A064084 a:= n-> mul(2^(i[1]^i[2])-1, i=ifactors(n)[2]):
%p A064084 seq(a(n), n=1..50); # _Alois P. Heinz_, Jun 09 2014
%t A064084 a[n_] := Times @@ (2^(Power @@@ FactorInteger[n]) - 1); Array[a, 40] (* _Amiram Eldar_, Aug 31 2023 *)
%o A064084 (PARI) a(n) = my(f=factor(n)); for (i=1, #f~, f[i,1] = 2^(f[i,1]^f[i,2])-1; f[i,2]=1); factorback(f); \\ _Michel Marcus_, Jun 09 2014
%Y A064084 Cf. A000225, A064085, A064086.
%K A064084 mult,easy,nonn
%O A064084 1,2
%A A064084 _Jens Voß_, Sep 04 2001
%E A064084 More terms from _Michel Marcus_, Jun 09 2014