A339915 Number of divisors of n with the same number of decimal digits as n.

1, 2, 2, 3, 2, 4, 2, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 1, 3, 2, 3, 1, 3, 2, 3, 2, 2, 1, 6, 1, 2, 2, 3, 2, 4, 1, 3, 2, 4, 1, 5, 1, 2, 3, 3, 2, 4, 1, 5, 2, 2, 1, 6, 2, 2, 2, 4, 1, 6, 2, 3, 2

Offset

1,2

Links

Table of n, a(n) for n=1..93.

Formula

a(n) = Sum_{d|n} [floor(log_10(d)) = floor(log_10(n))], where [ ] is the Iverson bracket.

Example

a(20) = 2; The only divisors of 20 that have the same number of digits as 20 are 10 and 20, so a(20) = 2.

Mathematica

Table[Sum[KroneckerDelta[Floor[Log10[i]], Floor[Log10[n]]] (1 - Ceiling[n/i] + Floor[n/i]), {i, n}], {n, 100}]

Prog

(PARI) a(n) = sumdiv(n, d, #Str(d) == #Str(n)); \\ Michel Marcus, Dec 22 2020

Crossrefs

Cf. A000005, A055642.

Sequence in context: A083903 A327536 A341946 * A306509 A083867 A076888

Adjacent sequences: A339912 A339913 A339914 * A339916 A339917 A339918

Keyword

nonn,base

Author

Wesley Ivan Hurt, Dec 22 2020

Status

approved