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Numbers n such that, in the prime factorization of n, the sum of the primes equals the squared sum of exponents.
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%I #10 Nov 08 2013 13:17:18

%S 28,98,132,198,351,368,726,1092,1375,1488,1521,1540,1638,2232,2295,

%T 2320,3008,3025,3348,3822,3825,3850,4048,4232,5022,5390,5800,6375,

%U 6591,6655,7098,7980,8470,11328,11375,11970,12012,12432,13005,14500,15925,16992,18018

%N Numbers n such that, in the prime factorization of n, the sum of the primes equals the squared sum of exponents.

%e 98 = 7^2 * 2, sum of primes is 9, sum of exponents is 3, so 98 is in the sequence.

%t t = {}; n = 1; While[Length[t] < 50, n++; {p, e} = Transpose[FactorInteger[n]]; If[Total[p] == Total[e]^2, AppendTo[t, n]]]; t (* _T. D. Noe_, Nov 08 2013 *)

%o (PARI) isok(n) = {f = factor(n); sum(i=1, #f~, f[i, 1]) == sum(i=1, #f~, f[i, 2])^2;} \\ _Michel Marcus_, Nov 07 2013

%Y Cf. A000040, A054411, A054412, A060205, A071174, A071175, A122406.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Nov 05 2013