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A337817 Smallest nonnegative number that has exactly n different representations as the product of a number and the sum of its decimal digits. 1
2, 0, 36, 900, 138600, 25336080, 3732276240, 240277237200 (list; graph; refs; listen; history; text; internal format)
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
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. A337051 (similar for Bogotá numbers), A337732.
Sequence in context: A172388 A193052 A347900 * A120489 A145576 A178235
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

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)