STATUS
proposed
approved
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Revision History for A019569
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Number of bar segments in a certain way of representing the integers graphically.
(history; published version)
(history; published version)
STATUS
editing
proposed
MATHEMATICA
a[n_] := a[n] = If[n<3, n-1, Function[l, Length[l] + Sum[a[l[[i, 2]]] + a[PrimePi[l[[i, 1]]] - If[i == 1, 0, PrimePi[l[[i-1, 1]]]]], {i, 1, Length[l]}]][SortBy[FactorInteger[n], First]]];
Array[a, 100] (* Jean-François Alcover, Nov 17 2020, after Alois P. Heinz *)
STATUS
approved
editing
STATUS
editing
approved
LINKS
Alois P. Heinz, <a href="/A019569/b019569.txt">Table of n, a(n) for n = 1..65536</a>
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
STATUS
proposed
editing
STATUS
editing
proposed
LINKS
Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a019/A019569
FORMULA
a(1) = 0; a(2) = 1; a(n) = 1 s + Sum_{i=1..s} ( a(e_i) + a(k_i - k_{i-1}) ).
EXTENSIONS
Formula corrected by Sean A. Irvine, Mar 26 2019
STATUS
approved
editing
AUTHOR
N. J. A. Sloane, _Simon Plouffe (simon.plouffe(AT)gmail.com)_
AUTHOR
_N. J. A. Sloane (njas(AT)research.att.com), _, Simon Plouffe (simon.plouffe(AT)gmail.com)