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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)[2], (x, y)-> x[1]<y[1])))

    end:

seq(a(n), n=1..100);  # Alois P. Heinz, Mar 26 2019

CROSSREFS

Sequence in context: A202472 A235613 A322418 * A003434 A330808 A097849

Adjacent sequences:  A019566 A019567 A019568 * A019570 A019571 A019572

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Simon Plouffe

EXTENSIONS

Formula corrected by Sean A. Irvine, Mar 26 2019

STATUS

approved

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