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%I #15 Mar 31 2021 12:04:11
%S 0,1,1,2,1,1,1,2,2,1,1,1,1,2,3,3,1,3,1,2,2,1,1,2,2,2,2,1,1,2,1,2,2,1,
%T 3,2,1,2,4,1,1,3,1,2,1,2,1,1,2,3,3,1,1,1,4,1,2,1,1,3,1,2,1,3,3,4,1,2,
%U 2,2,1,3,1,2,1,1,3,3,1,1,3,1,1,2,2,3,5,1,1,1,3,3,2,2,4,1,1,4,1
%N a(n) = A001222(A001414(n)).
%C a(n) is the number of prime divisors of the sum of prime divisors of n, counting multiplicity in both cases.
%H Robert Israel, <a href="/A342956/b342956.txt">Table of n, a(n) for n = 1..10000</a>
%e a(16) = 3 because A001414(16) = 2+2+2+2 = 8 and A001222(8) = A001222(2^3) = 3.
%p f:= proc(n) local t; numtheory:-bigomega(add(t[1]*t[2],t=ifactors(n)[2])) end proc:
%p map(f, [$1..100]);
%t Array[PrimeOmega[Plus@@Times@@@FactorInteger@#]&,100] (* _Giorgos Kalogeropoulos_, Mar 31 2021 *)
%o (Python)
%o from sympy import factorint
%o def A342956(n): return sum(factorint(sum(p*e for p, e in factorint(n).items())).values()) if n > 1 else 0 # _Chai Wah Wu_, Mar 31 2021
%Y Cf. A001222, A001414, A342957.
%K nonn
%O 1,4
%A _J. M. Bergot_ and _Robert Israel_, Mar 30 2021