%I A058313
%S A058313 1,1,5,7,47,37,319,533,1879,1627,20417,18107,263111,237371,52279,
%T A058313 95549,1768477,1632341,33464927,155685007,166770367,156188887,3825136961,
%U A058313 3602044091,19081066231,18051406831,57128792093,7751493599,236266661971
%N A058313 Numerator of the n-th alternating harmonic number, sum ((-1)^(k+1)/k, 
               k=1..n).
%C A058313 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
%H A058313 T. D. Noe, <a href="b058313.txt">Table of n, a(n) for n=1..200</a>
%H A058313 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/log2_000.htm">Factorizations of many number sequences</a>
%H A058313 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/log2_100.htm">Factorizations of many number sequences</a>
%H A058313 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HarmonicNumber.html">Harmonic Number</a>
%F A058313 G.f. for A058313(n)/ A058312(n) : log(1+x)/(1-x) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Jun 15 2003
%e A058313 1, 1/2, 5/6, 7/12, 47/60, 37/60, 319/420, 533/840, 1879/2520, ...
%p A058313 A058313 := n->numer(add((-1)^(k+1)/k,k=1..n));
%o A058313 (PARI) a(n)=(-1)^n*numerator(polcoeff(log(1-x)/(x+1)+O(x^(n+1)),n))
%Y A058313 Denominators are A058312. Cf. A025530.
%Y A058313 Apart from leading term, same as A075830.
%Y A058313 Cf. A001008 (numerator of n-th harmonic number).
%Y A058313 Bisections are A049281 and A082687.
%Y A058313 Sequence in context: A090520 A066219 A075830 this_sequence A120301 A119787 
               A025530
%Y A058313 Adjacent sequences: A058310 A058311 A058312 this_sequence A058314 A058315 
               A058316
%K A058313 nonn,frac,nice,easy
%O A058313 1,3
%A A058313 N. J. A. Sloane (njas(AT)research.att.com), Dec 09 2000