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%I #30 Mar 29 2021 15:03:15
%S 1,4,16,27,72,108,432,800,3125,6272,12500,21600,30375,50000,84375,
%T 121500,169344,225000,247808,337500,486000,750141,823543,1350000,
%U 1384448,3000564,3294172,6690816,12002256,13176688,19600000,22235661,37380096,37879808,59295096,88942644
%N Integers of the form Product p_j^k_j = Product k_j^p_j; p_j in A000040.
%C Fixed points of A008477.
%C a(3) = 16 is the only term of the form p^q with p <> q. - _Bernard Schott_, Mar 28 2021
%e 16 = 2^4 = 4^2.
%e 27 = 3^3.
%e 108 = 2^2*3^3.
%e 6272 = 2^7*7^2.
%e 121500 = 2^2 * 3^5*5^3.
%t f[n_] := Product[{p, e} = pe; e^p, {pe, FactorInteger[n]}];
%t Reap[For[n = 1, n <= 10^8, n++, If[f[n] == n, Print[n]; Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Mar 29 2021 *)
%o (PARI) for(n=2,10^8,if(n==prod(i=1,omega(n), component(component(factor(n),2),i)^component(component(factor(n),1),i)),print1(n,",")))
%Y Cf. A000040, A008477.
%Y Some subsequences: p_i^p_i (A051674), Product_i {p_i^p_i} (A048102), Product_(j,k)(p_j^p_k * p_k^p_j) with p_j < p_k (A082949) (see examples).
%K nonn
%O 1,2
%A _Olivier Gérard_
%E More terms from _David W. Wilson_
%E a(34)-a(36) from _Jean-François Alcover_, Mar 29 2021
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