A342956 - OEIS

%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