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 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). 5
 1, 5, 15, 45, 495, 16830, 4358970, 1159486020, 196818113950920, 3151092455396895169036800, 136084696980410308844836382925537725529600, 9996588705394796239042140065772174939073840705818917941136700639014745600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Dropping requirement a(n) > a(n-1) leads to a different partition: (1), (2, 3), (4, 5, 6), (7, 8), ... - see A160275. For partition starting with (1), (2), (3,4,5), see A075631. LINKS FORMULA a(n) = A000217(A079801(n)) - A000217(A079801(n-1)) [From R. J. Mathar and Max Alekseyev] PROG (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, May 06 2006 CROSSREFS Cf. A079799, A079800, A079801, A075631. Sequence in context: A176611 A001869 A058425 * A344814 A037504 A197237 Adjacent sequences:  A079795 A079796 A079797 * A079799 A079800 A079801 KEYWORD nonn AUTHOR Amarnath Murthy, Feb 05 2003 EXTENSIONS More terms from R. J. Mathar, May 06 2006 Edited and extended by Max Alekseyev, May 08 2009 STATUS approved

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Last modified August 11 00:55 EDT 2022. Contains 356046 sequences. (Running on oeis4.)