A096972 Number of preimages of n (or immediate predecessors) under map f(k) = k + (product of nonzero digits of k).

0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 1, 1, 0, 2, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 2, 1, 0, 1, 0, 1, 0, 2, 0, 0, 1, 2, 1, 1, 0, 1, 0, 0, 0, 2, 1, 0, 1, 1, 0, 2, 1, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 1, 1, 3, 0, 2, 0

Offset: 1

Author

Robert G. Wilson v, Jul 16 2004

Keywords

• easy
• nonn
• base

Links

• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A063108, A096347, A063425, A096922, A096923, A096924, A096925, A096926, A096927, A096928, A096929, A096930, A096931, A230106 (a variant).

Programs

Mathematica

f[n_] := Block[{s = Sort[ IntegerDigits[ n]]}, While[ s[[1]] == 0, s = Drop[s, 1]]; n + Times @@ s]; t = Table[0, {111}]; Do[ t[[f [n]]]++, {n, 111}]; Table[ t[[n]], {n, 105}]