A129476 a(n) is the concatenation in increasing order of all single-digit divisors of n.

1, 12, 13, 124, 15, 1236, 17, 1248, 139, 125, 1, 12346, 1, 127, 135, 1248, 1, 12369, 1, 1245, 137, 12, 1, 123468, 15, 12, 139, 1247, 1, 12356, 1, 1248, 13, 12, 157, 123469, 1, 12, 13, 12458, 1, 12367, 1, 124, 1359, 12, 1, 123468, 17, 125

Offset: 1

Author

Colin Pitrat (colin.pitrat(AT)rez-gif.supelec.fr), May 29 2007

Keywords

• nonn
• base
• easy

Comments

Sequence has period 2520 = 2^3 * 3^2 * 5 * 7.

a(n) = 1 iff n is a 11-rough number: not divisible by 2, 3, 5 or 7 (A008364). - Bernard Schott_, Dec 31 2020

Examples

			a(10)=125 because 1, 2 and 5 divides 10. 10 also divides 10 but it is not a digit so it doesn't appear.
a(2520) = 123456789. - Bernard Schott_, Dec 31 2020
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..5040

Crossrefs

Cf. A008364, A037278.

Programs

Maple

a:= n-> parse(cat(seq(`if`(irem(n, i)=0, i, [][]), i=1..9))):
seq(a(n), n=1..50);  # Alois P. Heinz, Dec 31 2020

Mathematica

Table[FromDigits[Select[Divisors[n],#<10&]],{n,50}] (* Harvey P. Dale, Jun 07 2015 *)

PARI

a(n) = fromdigits(select(x->(x<10), divisors(n))); \\ Michel Marcus, Dec 31 2020

Python

def a(n): return int('1'+"".join(d for d in "23456789" if n%int(d) == 0))
print([a(n) for n in range(1, 51)]) # Michael S. Branicky, Dec 31 2020

Formula

Let n be the rank and result be the number for this rank let a1...ak be k digits (a1...ak in [0,9]) result=a1*10^(k-1)...ak*10^0 with (i|n) => i in {a1...ak}.

Extensions

Editing and comment from Charles R Greathouse IV, Nov 02 2009

More terms from Harvey P. Dale, Jun 07 2015

Name edited by Joerg Arndt, Jan 01 2021