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%I #9 Jun 06 2024 08:23:33
%S 0,1,1,2,1,1,1,3,2,2,1,1,1,1,1,4,1,1,1,1,2,2,1,1,2,1,3,3,1,3,1,5,1,2,
%T 1,2,1,1,2,2,1,1,1,1,1,2,1,1,2,1,1,1,1,1,2,1,2,1,1,1,1,2,1,6,1,1,1,3,
%U 1,1,1,1,1,1,1,1,1,3,1,1,4,2,1,4,2,1,2,4,1,4,2,1,1,2,1,1,1,3,3,4,1,1,1,1,3
%N a(n) = gcd(bigomega(n), A056239(n)), where bigomega is number of prime factors with repetition, and A056239 is fully additive with a(p) = primepi(p).
%C As A001222 and A056239 are both fully additive sequences, all sequences that give the positions of multiples of some natural number k in this sequence are closed under multiplication, i.e., are multiplicative semigroups; for example A340784.
%H Antti Karttunen, <a href="/A373381/b373381.txt">Table of n, a(n) for n = 1..100000</a>
%F a(n) = gcd(A001222(n), A056239(n)).
%o (PARI)
%o A056239(n) = if(1==n, 0, my(f=factor(n)); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1])));
%o A373381(n) = gcd(bigomega(n), A056239(n));
%Y Cf. A001222, A056239, A340784 (positions of even terms), A353331 (their characteristic function).
%Y Cf. also A354871, A373370.
%K nonn
%O 1,4
%A _Antti Karttunen_, Jun 06 2024
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