%I A079798
%S A079798 1,5,15,45,495,16830,4358970,1159486020,196818113950920,
%T A079798 3151092455396895169036800,136084696980410308844836382925537725529600,
%U A079798 9996588705394796239042140065772174939073840705818917941136700639014745600
%N A079798 Partition of positive integers into shortest possible groups, starting 
               with (1), (2,3), (4,5,6), (7,8,9,10,11), such that a(n) = the sum 
               of the terms of the n-th group is a multiple of a(n-1) and a(n) > 
               a(n-1).
%C A079798 Dropping requirement a(n) > a(n-1) leads to a different partition: (1), 
               (2, 3), (4, 5, 6), (7, 8), ... - see A160275.
%C A079798 For partition starting with (1), (2), (3,4,5), see A075631.
%F A079798 a(n) = A000217(A079801(n)) - A000217(A079801(n-1)) [From R. J. Mathar 
               and Max Alekseyev]
%o A079798 (PARI) A000217(n)= { return(n*(n+1)/2) ; } upto(first,osum,strict)= { 
               local(trifirst,tstsu) ; trifirst=A000217(first-1) ; for(lst=first+1,
               first+100000000, tstsu=A000217(lst)-trifirst ; if(strict==1 && tstsu<= 
               osum, next ; ) ; if( tstsu % osum == 0, return(lst) ; ) ; ) ; return(-1) 
               ; } { a=1 ; first=2 ; for(n=2,40, last=upto(first,a,1) ; a=A000217(last)-A000217(first-1) 
               ; print(a,",") ; first=last+1 ; ) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               May 06 2006
%Y A079798 Cf. A079799, A079800, A079801, A075631.
%Y A079798 Sequence in context: A035069 A001869 A058425 this_sequence A037504 A105465 
               A089040
%Y A079798 Adjacent sequences: A079795 A079796 A079797 this_sequence A079799 A079800 
               A079801
%K A079798 nonn
%O A079798 1,2
%A A079798 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 05 2003
%E A079798 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 06 2006
%E A079798 Edited and extended by Max Alekseyev (maxale(AT)gmail.com), May 08 2009