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A258861
The pi-based antiderivative of n: the least m such that A258851(m) equals n.
6
0, 2, 3, 5, 4, 11, 13, 6, 19, 23, 29, 10, 8, 41, 43, 14, 53, 59, 61, 15, 12, 22, 79, 83, 89, 26, 21, 103, 107, 109, 25, 34, 16, 18, 139, 38, 151, 33, 163, 167, 173, 35, 181, 191, 28, 197, 199, 211, 223, 58, 229, 233, 24, 30, 27, 51, 49, 269, 55, 277, 281, 74
OFFSET
0,2
LINKS
FORMULA
a(n) = min { m >= 0 : A258851(m) = n }.
A258851(a(n)) = n.
a(n) <= A000040(n) for n>0.
MAPLE
with(numtheory):
d:= n-> n*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]):
a:= proc() local t, a; t, a:= -1, proc() -1 end;
proc(n) local h;
while a(n) = -1 do
t:= t+1; h:= d(t);
if a(h) = -1 then a(h):= t fi
od; a(n)
end
end():
seq(a(n), n=0..100);
MATHEMATICA
A258851[n_] := If[n == 0, 0, n*Total[Last[#]*PrimePi[First[#]]/First[#]& /@ FactorInteger[n]]];
a[n_] := For[m = 0, True, m++, If[A258851[m] == n, Return[m]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Sep 10 2023 *)
CROSSREFS
Column k=1 of A259016, A259153.
Sequence in context: A213648 A302849 A193971 * A171038 A023395 A316655
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 12 2015
STATUS
approved