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A058313
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Numerator of the n-th alternating harmonic number, sum ((-1)^(k+1)/k, k=1..n).
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42
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1, 1, 5, 7, 47, 37, 319, 533, 1879, 1627, 20417, 18107, 263111, 237371, 52279, 95549, 1768477, 1632341, 33464927, 155685007, 166770367, 156188887, 3825136961, 3602044091, 19081066231, 18051406831, 57128792093, 7751493599, 236266661971
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| A Wolstenholme-like theorem: for prime p > 3, if p = 6k-1, then p divides a(4k-1), otherwise if p = 6k+1, then p divides a(4k). - T. D. Noe (noe(AT)sspectra.com), Apr 01 2004
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..200
Hisanori Mishima, Factorizations of many number sequences
Hisanori Mishima, Factorizations of many number sequences
Eric Weisstein's World of Mathematics, Harmonic Number
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FORMULA
| G.f. for A058313(n)/ A058312(n) : log(1+x)/(1-x) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 15 2003
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EXAMPLE
| 1, 1/2, 5/6, 7/12, 47/60, 37/60, 319/420, 533/840, 1879/2520, ...
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MAPLE
| A058313 := n->numer(add((-1)^(k+1)/k, k=1..n));
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PROG
| (PARI) a(n)=(-1)^n*numerator(polcoeff(log(1-x)/(x+1)+O(x^(n+1)), n))
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CROSSREFS
| Denominators are A058312. Cf. A025530.
Apart from leading term, same as A075830.
Cf. A001008 (numerator of n-th harmonic number).
Bisections are A049281 and A082687.
Sequence in context: A066219 A174267 A075830 * A120301 A119787 A025530
Adjacent sequences: A058310 A058311 A058312 * A058314 A058315 A058316
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KEYWORD
| nonn,frac,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 09 2000
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