cp's OEIS Frontend

A008478 Integers of the form Product p_j^k_j = Product k_j^p_j; p_j in A000040.

%I A008478 #30 Mar 29 2021 15:03:15
%S A008478 1,4,16,27,72,108,432,800,3125,6272,12500,21600,30375,50000,84375,
%T A008478 121500,169344,225000,247808,337500,486000,750141,823543,1350000,
%U A008478 1384448,3000564,3294172,6690816,12002256,13176688,19600000,22235661,37380096,37879808,59295096,88942644
%N A008478 Integers of the form Product p_j^k_j = Product k_j^p_j; p_j in A000040.
%C A008478 Fixed points of A008477.
%C A008478 a(3) = 16 is the only term of the form p^q with p <> q. - _Bernard Schott_, Mar 28 2021
%e A008478 16 = 2^4 = 4^2.
%e A008478 27 = 3^3.
%e A008478 108 = 2^2*3^3.
%e A008478 6272 = 2^7*7^2.
%e A008478 121500 = 2^2 * 3^5*5^3.
%t A008478 f[n_] := Product[{p, e} = pe; e^p, {pe, FactorInteger[n]}];
%t A008478 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 A008478 (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 A008478 Cf. A000040, A008477.
%Y A008478 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 A008478 nonn
%O A008478 1,2
%A A008478 _Olivier Gérard_
%E A008478 More terms from _David W. Wilson_
%E A008478 a(34)-a(36) from _Jean-François Alcover_, Mar 29 2021