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The 3-adic valuation of sopfr(n), where sopfr is the sum of prime factors with repetition, A001414.
2

%I #6 Jul 02 2024 18:50:07

%S 0,1,0,0,0,0,1,1,0,0,0,0,2,0,0,0,0,0,2,0,0,0,2,0,1,2,0,0,0,0,0,0,0,1,

%T 0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,1,2,0,0,1,0,

%U 0,0,1,0,1,0,0,2,2,0,0,1,0,0,0,0,2,0,0,0,0,0,3,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,1,0,1,0,1,0,0,1,0,0,2

%N The 3-adic valuation of sopfr(n), where sopfr is the sum of prime factors with repetition, A001414.

%H Antti Karttunen, <a href="/A374217/b374217.txt">Table of n, a(n) for n = 2..100000</a>

%F a(n) = A007949(A001414(n)).

%o (PARI)

%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);

%o A374217(n) = valuation(A001414(n), 3);

%Y Cf. A001414, A007949, A289142 (gives the indices of nonzero terms here, after its initial 1), A373371

%Y Cf. also A374207, A374216.

%K nonn

%O 2,13

%A _Antti Karttunen_, Jul 02 2024