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A318323
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Numerators of rational valued sequence whose Dirichlet convolution with itself yields A046523, smallest number with same prime signature as n.
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2
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1, 1, 1, 3, 1, 2, 1, 5, 3, 2, 1, 5, 1, 2, 2, 35, 1, 5, 1, 5, 2, 2, 1, 4, 3, 2, 5, 5, 1, 9, 1, 63, 2, 2, 2, 35, 1, 2, 2, 4, 1, 9, 1, 5, 5, 2, 1, 55, 3, 5, 2, 5, 1, 4, 2, 4, 2, 2, 1, 9, 1, 2, 5, 231, 2, 9, 1, 5, 2, 9, 1, 43, 1, 2, 5, 5, 2, 9, 1, 55, 35, 2, 1, 9, 2, 2, 2, 4, 1, 9, 2, 5, 2, 2, 2, 49, 1, 5, 5, 35, 1, 9, 1, 4, 9
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OFFSET
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1,4
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COMMENTS
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The first 2^20 terms are positive.
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LINKS
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FORMULA
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a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A046523(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
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PROG
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(PARI)
up_to = 16384;
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&d<n, u[d]*u[n/d], 0)))/2); u}; \\ From A317937.
v318323_24 = DirSqrt(vector(up_to, n, A046523(n)));
A318323(n) = numerator(v318323_24[n]);
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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