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%I #7 Jun 02 2024 20:59:15
%S 1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
%T 1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,
%U 0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1
%N a(n) = 1 if A001414(n) and A276085(n) are both multiples of 3, otherwise 0, where A001414 is the sum of prime factors with repetition and A276085 is the primorial base log-function.
%H Antti Karttunen, <a href="/A373372/b373372.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = A373371(n) * A372573(n).
%F a(n) = [A373362(n) == 0 (mod 3)], where [ ] is the Iverson bracket.
%o (PARI)
%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
%o A002110(n) = prod(i=1,n,prime(i));
%o A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
%o A373372(n) = (!(A001414(n)%3) && !(A276085(n)%3));
%Y Characteristic function of A373373.
%Y Cf. A001414, A276086, A372573, A373362, A373371.
%Y Cf. also A373143.
%K nonn
%O 1
%A _Antti Karttunen_, Jun 02 2024
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