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%I #12 Apr 03 2023 10:36:12
%S 1,3,135,336,343,375,1134,14406,24336,41067,54756,85293,321408,428544,
%T 430080,1028196,1084752,1651104,1886976,2476656,2935296,3066336,
%U 3341637,3577392,4599504,4881384,5133375,5366088,5451264,8347248,8989344,9240075,9552816,9871875
%N Numbers k such that sigma(tau(k)) = rad(k).
%C rad(k) is the product of the primes dividing k (A007947), tau(k) is the number of divisors of k (A000005), sigma(k) is the sum of divisor of k (A000203).
%H Amiram Eldar, <a href="/A173582/b173582.txt">Table of n, a(n) for n = 1..100</a>
%H C. K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=Tau">The Prime Glossary, Number of divisors</a>
%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 A062069(k) = A007947(k).
%e tau(3) = 2, sigma(2) = 3 and rad(3) = 3. tau(135) = 8, sigma(8) = 15 and rad(135) = 15. tau(14406) = 20, sigma(20) = 42 and rad(14406) = 42.
%p with(numtheory):for n from 1 to 1000000 do : t1:= ifactors(n)[2] : t2 :=sum(t1[i][1], i=1..nops(t1)):if sigma(tau(n)) = t2 then print (n): else fi : od :
%t Select[Range[500000], DivisorSigma[1, DivisorSigma[0, #]] == Times @@ (First@# & /@ FactorInteger[#]) &] (* _Amiram Eldar_, Jul 11 2019 *)
%Y Cf. A000005, A000203, A007947, A062069.
%K nonn
%O 1,2
%A _Michel Lagneau_, Feb 22 2010
%E a(20)-a(34) from _Donovan Johnson_, Jan 14 2012
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