A248915 Composite numbers which divide the concatenation of their prime factors, with multiplicity, in descending order.

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

Links

Table of n, a(n) for n=1..8.

Michael S. Branicky, Python program for Andersen's algorithm extended to arbitrary base/ordering

StackExchange, New term in ascending order

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

Cf. A037276, A069872, A224930, A240265, A259047.

Sequence in context: A033699 A235544 A325848 * A225839 A221803 A289347

Adjacent sequences: A248912 A248913 A248914 * A248916 A248917 A248918

Keyword

nonn,more,base

Author

Paolo P. Lava, Oct 16 2014

Extensions

a(7)-a(8) from Giovanni Resta, Jun 16 2015

Status

approved