A337817 Smallest nonnegative number that has exactly n different representations as the product of a number and the sum of its decimal digits.

2, 0, 36, 900, 138600, 25336080, 3732276240, 240277237200

Offset

0,1

Comments

With "positive" instead "nonnegative", a(1) would be equal to 1, and other terms would not change.

a(8) <= 425616965373600. - Giovanni Resta, Oct 13 2022

Links

Table of n, a(n) for n=0..7.

Example

2 is the smallest number that is not possible to write as (m * sum of digits of m) for some m, hence a(0) = 2.
0 = 0 * 0, hence a(1) = 0
36 = 6 * 6 = 12 * (1+2) and 36 is the smallest number with 2 such representations, hence a(2) = 36.

Mathematica

f[n_] := n*Plus @@ IntegerDigits[n]; m = 2*10^5; v = Table[0, {m}]; Do[i = f[n] + 1; If[i <= m, v[[i]]++], {n, 0, m}]; s = {}; k = 0; While[(p = Position[v, k]) != {}, AppendTo[s, p[[1, 1]] - 1]; k++]; s (* Amiram Eldar, Sep 23 2020 *)

Prog

(PARI) a(n)={if(n==1, 0, for(k=1, oo, if(sumdiv(k, d, d*sumdigits(d)==k) == n, return(k))))} \\ Andrew Howroyd, Sep 23 2020

Crossrefs

Cf. A057147, A337816.

Cf. A337051 (similar for Bogotá numbers), A337732.

Sequence in context: A172388 A193052 A347900 * A120489 A145576 A178235

Adjacent sequences: A337814 A337815 A337816 * A337818 A337819 A337820

Keyword

nonn,base,more

Author

Bernard Schott, Sep 23 2020

Extensions

a(3)-a(5) from Amiram Eldar, Sep 23 2020

a(6)-a(7) from Bert Dobbelaere, Sep 27 2020, matching upper bounds from David A. Corneth

Status

approved