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%I #11 Apr 03 2023 10:36:11
%S 2,3,4,15,16,42,45,64,81,84,245,336,340,342,460,539,550,580,605,684,
%T 882,1012,1014,1160,1344,1360,1640,1674,1700,1785,1840,1972,2178,2254,
%U 2320,2322,2736,3096,3348,3645,4048,4096,4212,4332,4389,4400,4644,4830,5022
%N Numbers k such that tau(sigma(k)) = sopf(k).
%C 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 Amiram Eldar, <a href="/A173320/b173320.txt">Table of n, a(n) for n = 1..10000</a>
%H C. K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=Tau">The Prime Glossary, Number of divisors</a>
%H 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 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 k such that A062068(k)= A008472(k).
%e sigma(2) = 3, tau(3) = 2 and sopf(2) = 2 sigma(2254) = 4104, tau(4104) = 32 and sopf(2254) = 32.
%p 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 Select[Range[2,5100],DivisorSigma[0,DivisorSigma[1,#]]==Total[ FactorInteger[ #][[All,1]]]&] (* _Harvey P. Dale_, May 31 2019 *)
%Y Cf. A000005, A000203, A001414 (sopfr), A001222.
%K nonn
%O 1,1
%A _Michel Lagneau_, Feb 16 2010