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A343197 Numbers k such that A025281(k) is prime.

%I A343197 #13 Apr 09 2021 14:48:27
%S A343197 2,3,6,16,29,30,34,35,36,39,57,59,76,77,88,94,101,112,126,166,177,192,
%T A343197 206,228,238,248,251,258,259,260,271,275,276,282,299,317,318,333,345,
%U A343197 347,353,354,370,378,386,391,402,407,417,437,445,452,455,466,470,475,478,489,494,499,508,521,530
%N A343197 Numbers k such that A025281(k) is prime.
%C A343197 Numbers k such that A343196(k) = 1.
%H A343197 Robert Israel, <a href="/A343197/b343197.txt">Table of n, a(n) for n = 1..10000</a>
%e A343197 a(4) = 16 is a term because A025281(16) = A001414(16!) = 101.
%p A343197 sopf:= proc(n) local t; add(t[1]*t[2],t=ifactors(n)[2]) end proc:
%p A343197 R:= NULL: count:= 0: T:= 0:
%p A343197 for n from 2 while count < 100 do
%p A343197 T:= T + sopf(n);
%p A343197 if isprime(T) then R:= R, n; count:= count+1 fi;
%p A343197 od:
%p A343197 R;
%t A343197 Select[Range[2, 530], PrimeQ@ Total@ Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[#]] &[#!] &] (* _Michael De Vlieger_, Apr 07 2021 *)
%o A343197 (Python)
%o A343197 from sympy import isprime, factorint
%o A343197 A343197_list = [n for n in range(2,10**6) if isprime(sum(sum(p*e for p, e in factorint(i).items()) for i in range(2,n+1)))] # _Chai Wah Wu_, Apr 09 2021
%Y A343197 Cf. A001414, A025281, A343196.
%K A343197 nonn
%O A343197 1,1
%A A343197 _J. M. Bergot_ and _Robert Israel_, Apr 07 2021