A377712 a(n) is the least divisor of n with as many decimal digits as n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10, 21, 11, 23, 12, 25, 13, 27, 14, 29, 10, 31, 16, 11, 17, 35, 12, 37, 19, 13, 10, 41, 14, 43, 11, 15, 23, 47, 12, 49, 10, 17, 13, 53, 18, 11, 14, 19, 29, 59, 10, 61, 31, 21, 16, 13, 11, 67

Offset: 1

Author

Rémy Sigrist, Nov 04 2024

Keywords

• nonn
• base
• easy

Examples

			For n = 42: the divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42; the least divisor with 2 digits is 14, so a(42) = 14.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A055642, A109940.

Programs

Maple

f:= proc(n) local d,t;
  t:= ilog10(n);
  min(select(d -> ilog10(d)=t, numtheory:-divisors(n)))
end proc:
map(f, [$1..100]); # Robert Israel, Nov 06 2024

Mathematica

s={};Do[m=0;d=Divisors[n];Until[Length[IntegerDigits[d[[m]]]]==Length[IntegerDigits[n]],m++];AppendTo[s,d[[m]]],{n,67}];s (* James C. McMahon, Nov 06 2024 *)

PARI

a(n, base = 10) = { my (w = #digits(n, base)); forstep (x = base-1, 1, -1, if (n%x==0 && #digits(n/x)==w, return (n/x););); }

Python

def A377712(n): return n//next(d for d in range(n//10**(len(str(n))-1),0,-1) if not n%d) # Chai Wah Wu, Nov 06 2024

Formula

1 <= n/a(n) <= 9.