login
A240265
Numbers that divide the concatenation of their aliquot divisors, in ascending order.
5
1, 4, 15, 16, 255, 375, 495, 795, 1469, 3825, 9375, 28125, 66375, 67875, 234375, 249487, 286875, 309375, 337185, 450615, 590625, 628125, 1369125, 2390625, 2773125, 2781387, 3069375, 3706785, 4965309, 5859375, 12890625, 13539375, 26803125, 39607575, 62578125
OFFSET
1,2
COMMENTS
The sequence is infinite, because it contains all the numbers of the form 3*5^(2k+1). - Giovanni Resta, Apr 03 2014
EXAMPLE
Aliquot divisors of 1469 are 1, 13, 113. Their concatenation in ascending order is 113113 and 113113/1469 = 77.
MAPLE
with(numtheory);
T:=proc(t) local x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:
P:=proc(q) local a, b, c, d, i, k, n;
for n from 2 to q do a:=sort([op(divisors(n))]); b:=a[nops(a)-1];
for i from nops(a)-2 by -1 to 1 do b:=b+a[i]*10^T(b); od;
if type(b/n, integer) then print(n); fi;
od; end: P(10^6);
MATHEMATICA
Select[Range[6258*10^4], Divisible[FromDigits[Flatten[IntegerDigits/@ Most[ Divisors[ #]]]], #]&] (* Harvey P. Dale, Aug 21 2019 *)
CROSSREFS
Sequence in context: A228590 A103540 A065159 * A051956 A308983 A032826
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Apr 03 2014
EXTENSIONS
a(14)-a(34) from Giovanni Resta, Apr 03 2014
First term (a(1) = 1) prepended by Harvey P. Dale, Aug 21 2019
STATUS
approved