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A124876 Number of prime factors (counted with multiplicity) in factorization of A007408(n).

%I A124876 #14 Aug 28 2023 12:45:13
%S A124876 0,2,1,3,2,4,3,2,3,5,3,3,3,2,1,4,2,5,1,3,2,6,2,4,2,1,3,5,3,6,1,2,3,2,
%T A124876 3,10,4,4,5,5,8,7,7,2,4,7,3,2,4,3,2,5,3,4,2,8,3,4,4,5,3,3,7,2,5,10,4,
%U A124876 2,6,8,3,6,6,4,3,6,4,7,4,4,3,4,8,5,7,4
%N A124876 Number of prime factors (counted with multiplicity) in factorization of A007408(n).
%H A124876 Amiram Eldar, <a href="/A124876/b124876.txt">Table of n, a(n) for n = 1..106</a>
%F A124876 a(n) = A001222(A007408(n)). - _R. J. Mathar_, May 18 2007
%e A124876 a(1) = 0 since A007408(1) = 1 contains no prime factor,
%e A124876 a(2) = 2 since A007408(2) = 9 = 3 * 3,
%e A124876 a(3) = 1 since A007408(3) = 251 is prime,
%e A124876 a(6) = 4 since A007408(6) = 7 * 7 * 11 * 53.
%p A124876 seq( add(op(2,j),j=op(2,(ifactors@A007408)(n))), n=1..28 );
%p A124876 A001222 := proc(n) numtheory[bigomega](n) ; end: b := fscanf("b007408.txt","%d %d") : while b <> [] do printf("%d, ",A001222(op(2,b))) ; b := fscanf("b007408.txt","%d %d") : od : # _R. J. Mathar_, May 18 2007
%t A124876 Table[PrimeOmega[Numerator[Sum[1/k^3, {k, 1, n}]]], {n, 1, 50}] (* _Amiram Eldar_, Feb 09 2020 *)
%t A124876 PrimeOmega[Numerator[Accumulate[1/Range[50]^3]]] (* _Harvey P. Dale_, Aug 28 2023 *)
%Y A124876 Cf. A001222, A007408, A124877, A124787.
%K A124876 nonn
%O A124876 1,2
%A A124876 _M. F. Hasler_, Nov 11 2006
%E A124876 More terms from _R. J. Mathar_, May 18 2007
%E A124876 More terms from _Amiram Eldar_, Feb 09 2020