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A335660
a(n) = n - A334714(n).
2
0, 0, 0, 1, 1, 1, 1, 1, 2, 3, 3, 3, 2, 2, 2, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3, 4, 5, 5, 5, 4, 3, 3, 3, 4, 5, 5, 5, 5, 5, 4, 4, 3, 2, 2, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 3, 3, 3, 4, 5, 5, 5, 5, 5, 4, 4, 3, 2, 2, 3, 4, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 7
OFFSET
1,9
COMMENTS
a(n) >= 2 for n >= 9. (See Theorem 1.1. in Alkan, Booker & Luca.)
LINKS
Altug Alkan, Andrew R. Booker, and Florian Luca, On a recursively defined sequence involving the prime counting function, arXiv:2006.08013 [math.NT], 2020.
FORMULA
a(n) = n - Sum_{k=1..n} A335294(n).
MATHEMATICA
f[1] = 1; f[n_] := f[n] = PrimePi[n] - PrimePi[Sum[f[k], {k, 1, n - 1}]]; m = 100 ; Range[m] - Accumulate @ Array[f, m] (* Amiram Eldar, May 03 2021 *)
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Seiichi Manyama, Jun 17 2020
STATUS
approved