A258861 The pi-based antiderivative of n: the least m such that A258851(m) equals n.

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

Alois P. Heinz, Table of n, a(n) for n = 0..10000

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.

Cf. A000040, A000720, A258851, A258862, A258995.

Sequence in context: A213648 A302849 A193971 * A171038 A023395 A316655

Adjacent sequences: A258858 A258859 A258860 * A258862 A258863 A258864

Keyword

nonn

Author

Alois P. Heinz, Jun 12 2015

Status

approved