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 A275339 a(n) is the smallest number which has a water-capacity of n. 0
 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 Guy L. Steele, Four Solutions to a Trivial Problem, Google Tech Talk 12/1/2015. 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^f, f = op(2, ifactors(N)))]; n := nops(x); if n = 0 then return 0 fi; left := [seq(0, i=1..n)]; left := x; 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]]]; Array[a, 30] (* Jean-François Alcover, Jul 21 2019 *) CROSSREFS Sequence in context: A177871 A252953 A309315 * A049058 A056501 A056491 Adjacent sequences:  A275336 A275337 A275338 * A275340 A275341 A275342 KEYWORD nonn AUTHOR Peter Luschny, Aug 03 2016 STATUS approved

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Last modified November 14 17:24 EST 2019. Contains 329126 sequences. (Running on oeis4.)