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 A173320 #11 Apr 03 2023 10:36:11 %S A173320 2,3,4,15,16,42,45,64,81,84,245,336,340,342,460,539,550,580,605,684, %T A173320 882,1012,1014,1160,1344,1360,1640,1674,1700,1785,1840,1972,2178,2254, %U A173320 2320,2322,2736,3096,3348,3645,4048,4096,4212,4332,4389,4400,4644,4830,5022 %N A173320 Numbers k such that tau(sigma(k)) = sopf(k). %C A173320 sopf(k) is the sum of the distinct primes dividing k (A008472), tau(k) is the number of divisors of k (A000005), and sigma(k) is the sum of divisor of k (A000203). %H A173320 Amiram Eldar, <a href="/A173320/b173320.txt">Table of n, a(n) for n = 1..10000</a> %H A173320 C. K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=Tau">The Prime Glossary, Number of divisors</a> %H A173320 P. A. MacMahon, <a href="https://doi.org/10.1112/plms/s2-19.1.75">Divisors of numbers and their continuations in the theory of partitions</a>, Proc. London Math. Soc., 19 (1919), 75-113. %H A173320 Wacław Sierpiński, <a href="http://matwbn.icm.edu.pl/ksiazki/mon/mon42/mon4204.pdf">Number Of Divisors And Their Sum</a>, Elementary theory of numbers, Warszawa, 1964. %F A173320 k such that A062068(k)= A008472(k). %e A173320 sigma(2) = 3, tau(3) = 2 and sopf(2) = 2 sigma(2254) = 4104, tau(4104) = 32 and sopf(2254) = 32. %p A173320 with(numtheory): for n from 1 to 12000 do : t1:= ifactors(n)[2] : t2 :=sum(t1[i][1], i=1..nops(t1)): if tau(sigma(n)) = t2 then print (n): else fi : od : %t A173320 Select[Range[2,5100],DivisorSigma[0,DivisorSigma[1,#]]==Total[ FactorInteger[ #][[All,1]]]&] (* _Harvey P. Dale_, May 31 2019 *) %Y A173320 Cf. A000005, A000203, A001414 (sopfr), A001222. %K A173320 nonn %O A173320 1,1 %A A173320 _Michel Lagneau_, Feb 16 2010