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%I A248915 #48 Apr 14 2024 01:41:46
%S A248915 378,12467,95823,10715274,13485829,111495095,42002916561,176685987695
%N A248915 Composite numbers which divide the concatenation of their prime factors, with multiplicity, in descending order.
%C A248915 Prime numbers are not considered because they trivially satisfy the relation.
%C A248915 For terms in ascending order see A259047 and StackExchange link. [_Paolo P. Lava_, May 30 2019]
%C A248915 a(9) <= 3953318131772867. - _Chai Wah Wu_, Apr 12 2024
%C A248915 a(2), the bound for a(9) above, and larger terms may be found using an extension of Andersen's algorithm to arbitrary base and ordering (see links for an implementation and another term). - _Michael S. Branicky_, Apr 13 2024
%H A248915 Michael S. Branicky, <a href="/A259047/a259047.txt">Python program for Andersen's algorithm extended to arbitrary base/ordering</a>
%H A248915 StackExchange, <a href="http://math.stackexchange.com/questions/1166424/numbers-divide-its-prime-factors-concatenation">New term in ascending order</a>
%e A248915 Prime factors of 378 are 2,3,3,3,7; concat(7,3,3,3,2) = 73332 and 73332/378 = 194.
%p A248915 with(numtheory); P:=proc(q) local a,b,c,d,j,k,n;
%p A248915 for n from 1 to q do if not isprime(n) then a:=ifactors(n)[2]; b:=[]; d:=0;
%p A248915 for k from 1 to nops(a) do b:=[op(b),a[k][1]]; od; b:=sort(b);
%p A248915 for k from nops(a) by -1 to 1 do c:=1; while not b[k]=a[c][1] do c:=c+1; od;
%p A248915 for j from 1 to a[c][2] do d:=10^(ilog10(b[k])+1)*d+b[k]; od; od;
%p A248915 if type(d/n,integer) then print(n); fi;
%p A248915 fi; od; end: P(10^9);
%o A248915 (PARI) isok(n) = {my(s = ""); my(f = factor(n)); forstep (i=#f~, 1, -1, for (k=1, f[i,2], s = concat(s, Str(f[i,1])))); (eval(s) % n) == 0;} \\ _Michel Marcus_, Jun 16 2015
%Y A248915 Cf. A037276, A069872, A224930, A240265, A259047.
%K A248915 nonn,more,base
%O A248915 1,1
%A A248915 _Paolo P. Lava_, Oct 16 2014
%E A248915 a(7)-a(8) from _Giovanni Resta_, Jun 16 2015

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