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

Author

Paolo P. Lava, Oct 16 2014

Keywords

• nonn
• more
• base

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

Examples

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

Links

• Michael S. Branicky, Python program for Andersen's algorithm extended to arbitrary base/ordering
• StackExchange, New term in ascending order

Crossrefs

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

Programs

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);

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

Extensions

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