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A248915
Composite numbers which divide the concatenation of their prime factors, with multiplicity, in descending order.
6
378, 12467, 95823, 10715274, 13485829, 111495095, 42002916561, 176685987695
OFFSET
1,1
COMMENTS
Prime numbers are not considered because they trivially satisfy the relation.
For terms in ascending order see A259047 and StackExchange link. [Paolo P. Lava, May 30 2019]
a(9) <= 3953318131772867. - Chai Wah Wu, Apr 12 2024
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
EXAMPLE
Prime factors of 378 are 2,3,3,3,7; concat(7,3,3,3,2) = 73332 and 73332/378 = 194.
MAPLE
with(numtheory); P:=proc(q) local a, b, c, d, j, k, n;
for n from 1 to q do if not isprime(n) then a:=ifactors(n)[2]; b:=[]; d:=0;
for k from 1 to nops(a) do b:=[op(b), a[k][1]]; od; b:=sort(b);
for k from nops(a) by -1 to 1 do c:=1; while not b[k]=a[c][1] do c:=c+1; od;
for j from 1 to a[c][2] do d:=10^(ilog10(b[k])+1)*d+b[k]; od; od;
if type(d/n, integer) then print(n); fi;
fi; od; end: P(10^9);
PROG
(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
CROSSREFS
KEYWORD
nonn,more,base
AUTHOR
Paolo P. Lava, Oct 16 2014
EXTENSIONS
a(7)-a(8) from Giovanni Resta, Jun 16 2015
STATUS
approved