A248915 - OEIS

%I #48 Apr 14 2024 01:41:46

%S 378,12467,95823,10715274,13485829,111495095,42002916561,176685987695

%N Composite numbers which divide the concatenation of their prime factors, with multiplicity, in descending order.

%C Prime numbers are not considered because they trivially satisfy the relation.

%C For terms in ascending order see A259047 and StackExchange link. [_Paolo P. Lava_, May 30 2019]

%C a(9) <= 3953318131772867. - _Chai Wah Wu_, Apr 12 2024

%C 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 Michael S. Branicky, <a href="/A259047/a259047.txt">Python program for Andersen's algorithm extended to arbitrary base/ordering</a>

%H StackExchange, <a href="http://math.stackexchange.com/questions/1166424/numbers-divide-its-prime-factors-concatenation">New term in ascending order</a>

%e Prime factors of 378 are 2,3,3,3,7; concat(7,3,3,3,2) = 73332 and 73332/378 = 194.

%p with(numtheory); P:=proc(q) local a,b,c,d,j,k,n;

%p for n from 1 to q do if not isprime(n) then a:=ifactors(n)[2]; b:=[]; d:=0;

%p for k from 1 to nops(a) do b:=[op(b),a[k][1]]; od; b:=sort(b);

%p 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 for j from 1 to a[c][2] do d:=10^(ilog10(b[k])+1)*d+b[k]; od; od;

%p if type(d/n,integer) then print(n); fi;

%p fi; od; end: P(10^9);

%o (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 Cf. A037276, A069872, A224930, A240265, A259047.

%K nonn,more,base

%O 1,1

%A _Paolo P. Lava_, Oct 16 2014

%E a(7)-a(8) from _Giovanni Resta_, Jun 16 2015