A362675 Smallest number sharing n distinct (decimal) digits with its largest proper divisor.

11, 125, 1025, 3105, 37125, 251748, 2051748, 20491578, 204713568, 2046913578

Offset: 1

Author

Wesley Ivan Hurt, Apr 29 2023

Keywords

• nonn
• fini
• full
• base

Examples

			------------------------------------------------
  n   a(n)    Largest proper divisor of a(n)
------------------------------------------------
  1   11                 1
  2   125                25
  3   1025               205
  4   3105               1035
  5   37125              12375
  6   251748             125874
  7   2051748            1025874
  8   20491578           10245789
  9   204713568          102356784
 10   2046913578         1023456789
		

Crossrefs

Cf. A032742, A358076, A357929.

Programs

PARI

f(n) = n/factor(n)[1, 1]; \\ A032742
a(n) = my(k=2); while (#setintersect(Set(digits(k)), Set(digits(f(k)))) != n, k++); k; \\ Michel Marcus, Apr 29 2023

Python

from sympy import factorint
from itertools import count
def a(n):
    lb = 2*int("1023456789"[:n])
    return next(k for k in count(lb) if len(set(str(k)) & set(str(k//min(factorint(k))))) == n)
print([a(n) for n in range(1, 11)]) # Michael S. Branicky, Apr 29 2023

Extensions

a(9) from Michel Marcus, Apr 29 2023

a(10) from Michael S. Branicky, Apr 29 2023