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A349632 Dirichlet convolution of A250469 with A346234, which is Dirichlet inverse of A003961.

%I A349632 #19 Nov 29 2021 14:29:56
%S A349632 1,0,0,0,0,0,0,-6,0,6,0,-12,0,6,0,-18,0,-24,0,-24,0,24,0,0,0,24,-60,
%T A349632 -36,0,-48,0,-42,20,42,0,12,0,42,10,-12,0,-72,0,-60,-60,48,0,24,0,-42,
%U A349632 30,-72,0,84,0,-12,30,78,0,120,0,72,-120,-90,0,-180,0,-96,30,-132,0,48,0,96,-60,-108,0,-174,0,12,-120
%N A349632 Dirichlet convolution of A250469 with A346234, which is Dirichlet inverse of A003961.
%C A349632 Note that for n = 2..36, a(n) = -A349631(n).
%C A349632 Dirichlet convolution of this sequence with A003972 is A347376.
%H A349632 Antti Karttunen, <a href="/A349632/b349632.txt">Table of n, a(n) for n = 1..20000</a>
%H A349632 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A349632 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%F A349632 a(n) = Sum_{d|n} A250469(d) * A346234(n/d).
%o A349632 (PARI)
%o A349632 up_to = 20000;
%o A349632 A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));
%o A349632 ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
%o A349632 v078898 = ordinal_transform(vector(up_to,n,A020639(n)));
%o A349632 A078898(n) = v078898[n];
%o A349632 A250469(n) = if(1==n,n,my(spn = nextprime(1+A020639(n)), c = A078898(n), k = 0); while(c, k++; if((1==k)||(A020639(k)>=spn),c -= 1)); (k*spn));
%o A349632 A346234(n) = (moebius(n)*A003961(n));
%o A349632 A349632(n) = sumdiv(n,d,A250469(n/d)*A346234(d));
%Y A349632 Cf. A003961, A250469, A346234, A349631 (Dirichlet inverse).
%Y A349632 Cf. also A003972, A347376, A349382.
%Y A349632 Cf. also arrays A083221, A246278, A249821, A249822 and permutations A250245, A250246.
%K A349632 sign
%O A349632 1,8
%A A349632 _Antti Karttunen_, Nov 27 2021