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%I #19 Mar 22 2024 18:18:27
%S 1,2,111,112,5,11112,21112,1111112,111111111,10,110,11111111112,
%T 21112111111,112111111112,11111111115,11111111112112,211111111121111,
%U 11111111111111112,21111111211111111,20,21111111111111111111,21111111111111111112,211121111111111111111
%N Largest multiple of n as a concatenation of its partitions.
%C Any ordering of terms of the partition can be used before concatenation. - _D. S. McNeil_, May 09 2010
%H Chai Wah Wu, <a href="/A079840/b079840.txt">Table of n, a(n) for n = 1..49</a>
%e a(4) = 112: the partitions of 4 are 4,(3,1),(2,2),(1,1,2),(1,1,1,1). There are two multiples of 4, i.e., 4 and 112.
%e a(6) = 11112 (all partitions with one even part give multiples of 6 and 11112 is the largest).
%o (Python)
%o from collections import Counter
%o from operator import itemgetter
%o from sympy.utilities.iterables import partitions, multiset_permutations
%o def A079840(n):
%o smax, m = 0, 0
%o for s, p in sorted(partitions(n,size=True),key=itemgetter(0),reverse=True):
%o if s<smax:
%o break
%o if n % 10 or '0' in ''.join(str(d%10) for d in p):
%o for a in multiset_permutations(Counter(p).elements()):
%o if not (k:=int(''.join(str(d) for d in a))) % n:
%o m = max(k,m)
%o if m>0:
%o smax=s
%o return m # _Chai Wah Wu_, Feb 22 2024
%K nonn,base
%O 1,2
%A _Amarnath Murthy_, Feb 16 2003
%E Edited by _D. S. McNeil_, May 09 2010
%E At the suggestion of _Charles R Greathouse IV_, corrected and extended by _D. S. McNeil_, May 09 2010
%E a(22)-a(23) from _Chai Wah Wu_, Feb 22 2024
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