|
| |
|
|
A275339
|
|
a(n) is the smallest number which has a water-capacity of n.
|
|
1
|
|
|
|
60, 120, 440, 168, 264, 840, 2448, 528, 1904, 624, 1360, 2295, 816, 1632, 20128, 1824, 48300, 3105, 15392, 2208, 13024, 2400, 10656, 4080, 8288, 2784, 5920, 2976, 3552, 9120
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Define the water-capacity of a number as follows: If n has the prime factorization p1^e1*p2^e2*...*pk^ek let ci be a column of height pi^ei and width 1. Juxtaposing the ci leads to a bar graph which figuratively can be filled by water from the top. The water-capacity of a number is the maximum number of cells which can be filled with water.
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
For example 48300 has the prime factorization 2^2*3*5^2*7*23. The bar graph below has to be rotated counterclockwise for 90 degree.
2^2 ****
3 ***W
5^2 *************************
7 *******WWWWWWWWWWWWWWWW
23 ***********************
48300 is the smallest number which has a water-capacity of 17.
|
|
|
MAPLE
|
water_capacity := proc(N) option remember; local x, k, n, left, right, wc;
x := [seq(f[1]^f[2], f = op(2, ifactors(N)))]; n := nops(x);
if n = 0 then return 0 fi; left := [seq(0, i=1..n)]; left[1] := x[1];
for k from 2 to n do left[k] := max(left[k-1], x[k]) od;
right := [seq(0, i=1..n)]; right[n] := x[n];
for k from n-1 by -1 to 1 do right[k] := max(right[k+1], x[k]) od;
wc := 0; for k from 1 to n do wc := wc + min(left[k], right[k]) - x[k] od;
wc end:
a := proc(n, search_limit) local j;
for j from 1 to search_limit do if water_capacity(j) = n then return j fi od:
return 0; end: seq(a(n, 50000), n=1..30);
|
|
|
MATHEMATICA
|
w[k_] := With[{fi = Power @@@ FactorInteger[k]}, (fi //. {a___, b_, c__, d_, e___} /; AllTrue[{c}, # < b && # < d &] :> {a, b, Sequence @@ Table[ Min[b, d], {Length[{c}]}], d, e}) - fi // Total];
a[n_] := For[k = 1, True, k++, If[w[k] == n, Return[k]]];
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
