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 A008473 #49 Dec 08 2022 07:36:30
%S A008473 1,3,4,4,6,12,8,5,5,18,12,16,14,24,24,6,18,15,20,24,32,36,24,20,7,42,
%T A008473 6,32,30,72,32,7,48,54,48,20,38,60,56,30,42,96,44,48,30,72,48,24,9,21,
%U A008473 72,56,54,18,72,40,80,90,60,96,62,96,40,8,84,144,68,72,96,144,72,25,74,114
%N A008473 If n = Product (p_j^k_j) then a(n) = Product (p_j + k_j).
%C A008473 Coincides with sigma (A000203) for squarefree n. - _Franklin T. Adams-Watters_, Jan 31 2016
%C A008473 Every positive integer except 2 occurs in this sequence, but none occur infinitely often. For m > 4, there are n > m with a(n) = m. This implies that every integer greater than 4 occurs in the iterated sequence infinitely often. For example, 5 <- 8 <- 125 <- 113^12 <- .... - _Franklin T. Adams-Watters_, Jan 31 2016
%C A008473 Sum of the powerfree parts of the divisors of n. - _Wesley Ivan Hurt_, Jun 13 2021
%H A008473 Vincenzo Librandi, <a href="/A008473/b008473.txt">Table of n, a(n) for n = 1..10000</a>
%F A008473 Multiplicative with a(p^e) = p+e. - _David W. Wilson_, Aug 01 2001
%F A008473 a(n) = Product_{k=1..A001221(n)} (A027748(n,k) + A124010(n,k)). - _Reinhard Zumkeller_, Jul 17 2014
%F A008473 a(n)/A007947(n) = A322965(n)/A322966(n). - _David S. Metzler_, Jan 01 2019
%F A008473 a(n) = Sum_{d|n} A055231(d). - _Wesley Ivan Hurt_, Jun 13 2021
%F A008473 Sum_{k=1..n} a(k) ~ c * n^2, where c = (Pi^4/72) * Product_{p prime} (1 - 2/p^2 + 2/p^4 - 1/p^5) = 0.5342800948... . - _Amiram Eldar_, Dec 08 2022
%p A008473 A008473 := proc(n) local e,j; e := ifactors(n)[2]:
%p A008473 mul (e[j][1]+e[j][2], j=1..nops(e)) end:
%p A008473 seq (A008473(n), n=1..80);
%p A008473 # _Peter Luschny_, Jan 17 2011
%t A008473 Array[Times @@ Total /@ FactorInteger[ # ] &, 80] (* Joseph Biberstine (jrbibers(AT)indiana.edu), Jul 28 2006 *)
%o A008473 (Haskell)
%o A008473 a008473 n = product $ zipWith (+) (a027748_row n) (a124010_row n)
%o A008473 -- _Reinhard Zumkeller_, Jul 17 2014
%o A008473 (PARI) a(n)=my(f = factor(n)); for (k=1, #f~, f[k, 1] = f[k, 1] + f[k, 2]; f[k, 2] = 1;); factorback(f); \\ _Michel Marcus_, Jan 31 2016
%Y A008473 Cf. A027748, A124010, A001221, A203908, A000203, A322965, A322966.
%Y A008473 Cf. A055231 (powerfree part of n).
%K A008473 nonn,mult
%O A008473 1,2
%A A008473 _Olivier Gérard_
%E A008473 More terms from Joseph Biberstine (jrbibers(AT)indiana.edu), Jul 28 2006