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A342956
a(n) = A001222(A001414(n)).
3
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, 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, 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
OFFSET
1,4
COMMENTS
a(n) is the number of prime divisors of the sum of prime divisors of n, counting multiplicity in both cases.
LINKS
EXAMPLE
a(16) = 3 because A001414(16) = 2+2+2+2 = 8 and A001222(8) = A001222(2^3) = 3.
MAPLE
f:= proc(n) local t; numtheory:-bigomega(add(t[1]*t[2], t=ifactors(n)[2])) end proc:
map(f, [$1..100]);
MATHEMATICA
Array[PrimeOmega[Plus@@Times@@@FactorInteger@#]&, 100] (* Giorgos Kalogeropoulos, Mar 31 2021 *)
PROG
(Python)
from sympy import factorint
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
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Mar 30 2021
STATUS
approved