A338505 Number of positive integers less than n with the same product of decimal digits as n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 3, 2, 1, 0, 1, 0, 0, 0, 3, 3, 3, 2, 1, 0, 1, 0, 0, 0, 4, 2, 1, 1, 1, 0, 0, 0, 0, 0, 5, 4, 3, 2, 2, 1, 1, 0, 0, 0, 6, 2, 1, 1, 1, 1, 1, 0, 0, 0, 7, 4, 2, 3, 1, 1, 1, 1, 0, 0, 8

Offset: 1

Author

Ilya Gutkovskiy, Oct 31 2020

Keywords

• nonn
• base

Examples

			a(22) = 2 because A007954(22) = 4 and also A007954(4) = A007954(14) = 4.
		

Crossrefs

Cf. A007954, A138471, A254524.

Programs

Mathematica

Table[Length[Select[Range[n - 1], Times @@ IntegerDigits@# == Times @@ IntegerDigits@n &]], {n, 90}]

PARI

a(n)={my(t=vecprod(digits(n))); sum(k=1, n-1, vecprod(digits(k))==t)} \\ Andrew Howroyd, Oct 31 2020

Formula

a(n) = |{0 < j < n : A007954(j) = A007954(n)}|.

Extensions

Definition clarified by Ilya Gutkovskiy, Apr 14 2022