A349632 Dirichlet convolution of A250469 with A346234, which is Dirichlet inverse of A003961.
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, -36, 0, -48, 0, -42, 20, 42, 0, 12, 0, 42, 10, -12, 0, -72, 0, -60, -60, 48, 0, 24, 0, -42, 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
Offset: 1
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PARI
up_to = 20000; A020639(n) = if(1==n,n,vecmin(factor(n)[, 1])); 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; }; v078898 = ordinal_transform(vector(up_to,n,A020639(n))); A078898(n) = v078898[n]; 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)); A346234(n) = (moebius(n)*A003961(n)); A349632(n) = sumdiv(n,d,A250469(n/d)*A346234(d));
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