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

1,21

Links

Table of n, a(n) for n=1..90.

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A007954, A138471, A254524.

Sequence in context: A295854 A230630 A343957 * A037867 A122879 A037866

Adjacent sequences: A338502 A338503 A338504 * A338506 A338507 A338508

Keyword

nonn,base

Author

Ilya Gutkovskiy, Oct 31 2020

Extensions

Definition clarified by Ilya Gutkovskiy, Apr 14 2022

Status

approved