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%I #17 Mar 20 2019 17:10:13
%S 8580,16632,24840,35910,38280,53130,161040,186732,276276,429780,
%T 598290,833112,1232616,1297890,1631448,2661330,2781000,2875740,
%U 3111108,3233790,3449640,3504816,3754920,4901160,5185488,5211570,5948250,6749028,8066640,9006984,10750080
%N Number x such that sigma(x) = Sum_{i=1..k} {sigma(x/p_i)}, where p_i are the k prime factors of x.
%H Amiram Eldar, <a href="/A324711/b324711.txt">Table of n, a(n) for n = 1..100</a>
%e Prime factors of 8580 are 2, 3, 5, 11, 13 and sigma(8580) = 28224, sigma(8580/2) + sigma(8580/3) + sigma(8580/5) + sigma(8580/11) + sigma(8580/13) = 12096 + 7056 + 4704 + 2352 + 2016 = 28224.
%p with(numtheory): P:=proc(q) local k,n; for n from 1 to q do
%p if sigma(n)=add(sigma(n/k),k=factorset(n)) then print(n);
%p fi; od; end: P(10^9);
%t Select[Range[2, 60000], DivisorSigma[1, #] == Total@DivisorSigma[1, #/FactorInteger[#][[;; , 1]]] &] (* _Amiram Eldar_, Mar 20 2019 *)
%o (PARI) isok(x) = my(f=factor(x)[,1]~); sigma(x) == sum(k=1, #f, sigma(x/f[k])); \\ _Michel Marcus_, Mar 15 2019
%Y Cf. A000203, A324710.
%K nonn
%O 1,1
%A _Paolo P. Lava_, Mar 13 2019
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