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 A019569 Number of bar segments in a certain way of representing the integers graphically. 1
 0, 1, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 4, 3, 5, 4, 5, 4, 4, 4, 4, 5, 5, 5, 4, 4, 5, 5, 4, 5, 4, 4, 4, 4, 6, 6, 4, 4, 5, 6, 5, 5, 5, 4, 4, 5, 5, 3, 6, 5, 5, 5, 6, 4, 5, 5, 5, 6, 4, 6, 4, 5, 5, 5, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Let p(i) = i-th prime. Let n = Product_{i=1..s} p(k_i)^e_i with k_1 < k_2 < ... < k_s. The drawing of n=1 is a blank space. The drawing of n > 1 is arranged around a horizontal bar divided by s-1 scores into s segments. The scores and the bar divide the space above and below the bar into 2's compartments. In the i-th compartment above the bar place the drawing of e_i and in the i-th compartment below the bar place the drawing of k_i - k_{i-1}. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..65536 Sean A. Irvine, Java program (github) Tyler Pierce, A way of drawing natural numbers FORMULA a(1) = 0; a(2) = 1; a(n) = s + Sum_{i=1..s} ( a(e_i) + a(k_i - k_{i-1}) ) with k_0 = 0. MAPLE with(numtheory): a:= proc(n) option remember; `if`(n<3, n-1, (l-> nops(l)+       add(a(l[i, 2])+a(pi(l[i, 1])-`if`(i=1, 0, pi(l[i-1, 1]))),       i=1..nops(l)))(sort(ifactors(n), (x, y)-> x

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Last modified September 23 04:20 EDT 2020. Contains 337294 sequences. (Running on oeis4.)