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

1,2

Comments

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

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A054055 (largest digit of n).

Sequence in context: A028899 A081595 A122644 * A363372 A028900 A081596

Adjacent sequences: A209925 A209926 A209927 * A209929 A209930 A209931

Keyword

nonn,base

Author

Jaroslav Krizek, Mar 20 2012

Status

approved