A339915 - OEIS

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

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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