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A354365
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Numerators of Dirichlet inverse of primorial deflation fraction A319626(n) / A319627(n).
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8
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1, -2, -3, 0, -5, 3, -7, 0, 0, 10, -11, 0, -13, 14, 5, 0, -17, 0, -19, 0, 21, 22, -23, 0, 0, 26, 0, 0, -29, -5, -31, 0, 33, 34, 7, 0, -37, 38, 39, 0, -41, -21, -43, 0, 0, 46, -47, 0, 0, 0, 51, 0, -53, 0, 55, 0, 57, 58, -59, 0, -61, 62, 0, 0, 65, -33, -67, 0, 69, -14, -71, 0, -73, 74, 0, 0, 11, -39, -79, 0, 0, 82
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OFFSET
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1,2
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COMMENTS
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Because the ratio n / A064989(n) = A319626(n) / A319627(n) is multiplicative, so is also its Dirichlet inverse (which also is a sequence of rational numbers). This sequence gives the numerators when presented in its lowest terms, while A354366 gives the denominators. See the examples.
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LINKS
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FORMULA
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EXAMPLE
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The ratio a(n)/A354366(n) for n = 1..22: 1, -2, -3/2, 0, -5/3, 3, -7/5, 0, 0, 10/3, -11/7, 0, -13/11, 14/5, 5/2, 0, -17/13, 0, -19/17, 0, 21/10, 22/7.
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PROG
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(PARI)
A064989(n) = { my(f = factor(n)); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
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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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