A228286 Smallest x + y*z, given x*y + z = n (for positive integers x, y, z).
2, 3, 4, 4, 6, 5, 7, 6, 6, 7, 9, 7, 10, 9, 8, 8, 12, 9, 12, 9, 10, 13, 15, 10, 10, 15, 12, 11, 15, 11, 16, 12, 14, 17, 12, 12, 17, 21, 16, 13, 18, 13, 19, 15, 14, 19, 24, 14, 14, 15, 20, 17, 21, 15, 16, 15, 22, 25, 28, 16, 22, 27, 16, 16, 18, 17, 23, 21, 25, 17
Offset: 2
Examples
For n = 160, a(n) = 50, as 26 * 6 + 4 = 160 and 26 + 6 * 4 = 50 and no triple of positive integers (x, y, z) with xy + z = 160 gives a smaller value for x + yz.
Links
- Peter Kagey, Table of n, a(n) for n = 2..10000
Crossrefs
Programs
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Maple
A228286 := proc(n) local a,x,y,z ; a := n+n^2 ; for z from 1 to n-1 do for x in numtheory[divisors](n-z) do y := (n-z)/x ; a := min(a, x+y*z) ; end do: end do: return a; end proc: # R. J. Mathar, Sep 02 2013
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Mathematica
a[n_] := Module[{X, bX, bT, m}, bT = n + 1; bX = {n - 1, 1, 1, n}; X = bX; m = Floor[2*Sqrt[X[[3]]*(n - X[[3]])]]; While[bT >= m && X[[3]] <= n/2, X[[2]] = Max[1, Floor[(n - bX[[3]])/bT]]; While[X[[2]] <= Floor[bT/X[[3]]], If[Mod[n - X[[3]], X[[2]]] == 0, X[[1]] = (n - X[[3]])/X[[2]]; X[[4]] = X[[1]] + X[[2]]*X[[3]]; If[X[[4]] < bX[[4]], bX = X]]; X[[2]] = X[[2]] + 1]; X[[3]] = X[[3]] + 1; m = Floor[2*Sqrt[X[[3]]*(n - X[[3]])]]]; Return[bX]]; Table[a[n][[-1]], {n, 2, 100}]
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