A209928 Largest digit of all divisors of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 5, 1, 6, 3, 7, 5, 8, 7, 9, 9, 5, 7, 2, 3, 8, 5, 6, 9, 8, 9, 6, 3, 8, 3, 7, 7, 9, 7, 9, 9, 8, 4, 7, 4, 4, 9, 6, 7, 8, 9, 5, 7, 6, 5, 9, 5, 8, 9, 9, 9, 6, 6, 6, 9, 8, 6, 6, 7, 8, 9, 7, 7, 9, 7, 7, 7, 9, 7, 9, 9, 8, 9, 8, 8, 8, 8, 8, 9

Offset: 1

Author

Jaroslav Krizek, Mar 20 2012

Keywords

• nonn
• base

Comments

Also largest digit of concatenation of all divisors of n (A037278, A176558).

a(n) = 9 for almost all n. - Charles R Greathouse IV, Mar 20 2012

With an offset of 1 rather than 0, A016186 tells us how many integers among the first 10^n have 9s among their digits, and those numbers are therefore guaranteed to index a 9 in this sequence. More interesting of course are those numbers that don't have a 9 in their own digits but do have a 9 among the digits of their nontrivial divisors. - Alonso del Arte, Mar 23 2012

Examples

			a(12) = 6 because digit 6 is largest digit of all divisors of 12: (1, 2, 3, 4, 6, 12).
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054055 (largest digit of n).

Programs

Mathematica

Flatten[Table[Take[Sort[Flatten[IntegerDigits[Divisors[n]]]], -1], {n, 100}]] (* Alonso del Arte, Mar 23 2012 *)

PARI

a(n)=my(t);fordiv(n, d, t=max(t, vecmax(eval(Vec(Str(d))))); if(t>8, return(t)));t \\Charles R Greathouse IV, Mar 20 2012

Python

from sympy import divisors
def a(n): return int(max("".join(map(str, divisors(n)))))
print([a(n) for n in range(1, 88)]) # Michael S. Branicky, Feb 22 2021