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A374132 The 2-adic valuation of A276085(n), where A276085 is the primorial base log-function.

%I A374132 #6 Jun 30 2024 16:13:10
%S A374132 0,1,1,1,0,1,0,2,0,1,2,1,0,3,2,1,0,1,3,5,0,1,0,2,0,1,5,1,0,1,0,2,0,2,
%T A374132 1,1,0,3,0,1,0,1,2,1,0,1,1,2,0,4,3,1,0,3,0,4,0,1,1,1,0,1,1,2,0,1,4,2,
%U A374132 0,1,0,1,0,1,4,4,0,1,1,3,0,1,1,2,0,3,0,1,0,2,2,4,0,2,0,1,0,1,1,1,0,1,0,1,0,1,3
%N A374132 The 2-adic valuation of A276085(n), where A276085 is the primorial base log-function.
%H A374132 Antti Karttunen, <a href="/A374132/b374132.txt">Table of n, a(n) for n = 2..100000</a>
%F A374132 a(n) = A007814(A276085(n)).
%o A374132 (PARI)
%o A374132 A276085(n) = { my(f=factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
%o A374132 A374132(n) = valuation(A276085(n),2);
%Y A374132 Cf. A007814, A276085.
%Y A374132 Cf. A036554 (indices of 0's), A003159 (of nonzero terms), A373142 (of 1's), A373267 (of 2's), A369002 (of terms >= 2), A373138 (of terms >= 3).
%Y A374132 Cf. also A374133.
%K A374132 nonn
%O A374132 2,8
%A A374132 _Antti Karttunen_, Jun 30 2024