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 A126164 #16 Feb 16 2025 08:33:04
%S A126164 0,0,0,2,0,0,0,2,3,0,0,6,0,0,0,6,0,6,0,10,0,0,0,6,5,0,3,14,0,0,0,2,0,
%T A126164 0,0,36,0,0,0,10,0,0,0,22,15,0,0,18,7,10,0,26,0,6,0,14,0,0,0,30,0,0,
%U A126164 21,14,0,0,0,34,0,0,0,48,0,0,15
%N A126164 Sum of the proper exponential divisors of n.
%C A126164 The e-divisors (or exponential divisors) of x=Product p(i)^r(i) are all numbers of the form Product p(i)^s(i) where s(i) divides r(i) for all i.
%H A126164 Antti Karttunen, <a href="/A126164/b126164.txt">Table of n, a(n) for n = 1..10000</a>
%H A126164 Ant King, <a href="/A126164/a126164.pdf">Mathematica programs for A126164 - A126166</a>.
%H A126164 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/e-Divisor.html">e-Divisor</a>.
%F A126164 a(n) = esigma(n) - n = A051377(n) - n.
%e A126164 The exponential divisors of 240 are 30, 60 and 240, so a(240) = 30+60 = 90.
%t A126164 f[p_, e_] := DivisorSum[e, p^# &]; a[1] = 0; a[n_] := Times @@ f @@@ FactorInteger[n] - n; Array[a, 100] (* _Amiram Eldar_, Aug 13 2023 *)
%o A126164 (PARI)
%o A126164 A051377(n) = { my(f=factor(n)); prod(i=1, #f[, 1], sumdiv(f[i, 2], d, f[i, 1]^d)); }; \\ This function from _Charles R Greathouse IV_, Nov 22 2011
%o A126164 A126164(n) = (A051377(n) - n); \\ _Antti Karttunen_, Oct 04 2017, after the given formula
%Y A126164 Cf. A051377, A049419, A054979, A054980, A126168.
%K A126164 easy,nonn
%O A126164 1,4
%A A126164 _Ant King_, Dec 21 2006