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A317927
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Numerators of rational valued sequence whose Dirichlet convolution with itself yields A005187.
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4
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1, 3, 2, 19, 4, 2, 11, 63, 6, 3, 19, 13, 23, 17, 5, 867, 16, 4, 35, 5, 17, 25, 21, 11, 31, 29, 13, 113, 27, 13, 57, 3069, 13, 9, 23, 25, 71, 41, 14, 69, 79, 33, 41, 169, 9, 25, 89, 615, 259, 53, 17, 197, 51, 25, 29, 389, 20, 31, 113, 59, 117, 67, 10, 22199, 18, 14, 131, 31, 51, 71, 69, 11, 143, 77, 22, 281, 91, 35, 153, 489, 71, 85, 81, 151, 19
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OFFSET
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1,2
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COMMENTS
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The first negative term is a(330) = -21.
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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) * (A005187(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)
A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
A317927perA317928(n) = if(1==n, n, (A005187(n)-sumdiv(n, d, if((d>1)&&(d<n), A317927perA317928(d)*A317927perA317928(n/d), 0)))/2);
A317927(n) = numerator(A317927perA317928(n));
(PARI)
\\ Memoized implementation:
memo = Map();
A317927perA317928(n) = if(1==n, n, if(mapisdefined(memo, n), mapget(memo, n), my(v = (A005187(n)-sumdiv(n, d, if((d>1)&&(d<n), A317927perA317928(d)*A317927perA317928(n/d), 0)))/2); mapput(memo, n, v); (v)));
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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STATUS
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approved
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