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Numbers k such that k = Product (p_j^e_j) = Sum (prime(p_j)^e_j).
1

%I #8 May 09 2018 23:04:18

%S 20,68,76,92,8248

%N Numbers k such that k = Product (p_j^e_j) = Sum (prime(p_j)^e_j).

%C Fixed points of A304251.

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

%e 68 is a term because 68 = 2^2*17 = prime(1)^2*prime(7) = prime(prime(1))^2 + prime(prime(7)).

%e 8248 is a term because 8248 = 2^3*1031 = prime(1)^3*prime(173) = prime(prime(1))^3 + prime(prime(173)).

%t a[n_] := Plus @@ (Prime[#[[1]]]^#[[2]] & /@ FactorInteger[n]); Select[Range[10000], a[#] == # &]

%o (PARI) isok(n) = my(f=factor(n)); n == sum(k=1, #f~, prime(f[k,1])^f[k,2]); \\ _Michel Marcus_, May 09 2018

%Y Cf. A006450, A008478, A048768, A304194, A304251.

%K nonn,more

%O 1,1

%A _Ilya Gutkovskiy_, May 09 2018