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1, 1, 1, 2, 1, 1, 1, 0, 5, 1, 1, -4, 1, 1, 1, 4, 1, -3, 1, -28, 1, 1, 1, -12, 41, 1, -19, -508, 1, 1, 1, 2, 1, 1, 1, 14, 1, 1, 1, -60, 1, 1, 1, -131068, -115, 1, 1, -2, 3281, -39, 1, -8589934588, 1, -51, 1, -1020, 1, 1, 1, -124, 1, 1, -2035, 6, 1, 1, 1, -36893488147419103228, 1, 1, 1, -12, 1, 1, -199, -680564733841876926926749214863536422908
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OFFSET
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1,4
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LINKS
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FORMULA
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For all n, a(A005117(n)) = 1. [It is not known if there are 1's in any other positions. See Jianing Song's Oct 13 2019 comment in A033879.]
For a necessary condition that a(s) would be zero for any square, see A331741.
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PROG
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(PARI)
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A331734(n) = if(issquarefree(n), 1, my(f=factor(n), u=#binary(vecmax(f[, 2])), prods=vector(u, x, 1), m=1, e); for(i=1, u, for(k=1, #f~, if(bitand(f[k, 2], m), prods[i] *= f[k, 1])); m<<=1); (2*prod(i=1, u, prime(i)^A048675(prods[i]))) - prod(i=1, u, (prime(i)^(1+A048675(prods[i]))-1)/(prime(i)-1)));
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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