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A318664
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Numerators of the sequence whose Dirichlet convolution with itself yields A064664, the inverse permutation of EKG-sequence.
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3
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1, 1, 5, 1, 5, -1, 7, 3, -1, -1, 10, 3, 14, -1, -7, 5, 33, 59, 37, 9, -10, -1, 43, -1, -1, -1, 181, 13, 57, 89, 61, 15, -29, -1, -45, 31, 67, -1, -41, 1, 37, 129, 81, 11, 301, -1, 89, 21, 1, 26, -97, 10, 50, -93, -47, -5, -109, -1, 107, -33, 115, -1, 411, 15, -43, 201, 64, 33, -127, 56, 67, 181, 69, -1, 283, 35, -31, 255, 151, 7
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OFFSET
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1,3
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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) * (A064664(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)
v064413 = readvec("b064413_upto65539_terms_only.txt"); \\ From b-file of A064413 prepared beforehand.
m064664 = Map();
for(n=1, 65539, mapput(m064664, A064413(n), n));
up_to = (2^14);
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.
v318664_65 = DirSqrt(vector(up_to, n, A064664(n)));
A318664(n) = numerator(v318664_65[n]);
A318665(n) = denominator(v318664_65[n]);
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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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