%I #12 May 09 2018 23:03:50

%S 1,2,12,56,180,304,336,936,1696,1824,2484,5040,5328,6664,8384,8512,

%T 9900,10176,13176,14040,25632,26208,27360,33372,33712,37260,39808,

%U 39984,47488,50304,51072,52200,65232,69552,79920,126900,128448,142272,149184,152640,162648,167776,184064,193752,197640

%N Numbers k such that k = Product (p_j^e_j) = Product (pi(p_j)*p_j), where pi() = A000720.

%C Numbers k such that A007947(k)*A156061(k) = k or A156061(k) = A003557(k).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%e 9900 is a term because 9900 = 2^2 * 3^2 * 5^2 * 11 = prime(1)^2 * prime(2)^2 * prime(3)^2 * prime(5) = 1*prime(1) * 2*prime(2) * 3*prime(3) * 5*prime(5).

%t a[n_] := Times @@ (PrimePi[#[[1]]] #[[1]] & /@ FactorInteger[n]); a[1] = 1; Select[Range[200000], a[#] == # &]

%o (PARI) isok(n) = {my(f=factor(n)); prod(k=1, #f~, primepi(f[k,1])*f[k,1]) == n;} \\ _Michel Marcus_, May 08 2018

%Y Cf. A000720, A003557, A005117, A007947, A008478, A033286, A046022, A048768, A078779, A109298, A156061.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, May 07 2018