A258995 Third pi-based antiderivative of n: the least m such that A258851^3(m) equals n.

0, 5, 11, 10, 4, 29, 35, 41, 14, 431, 599, 78, 15, 38, 201, 191, 25, 382, 186, 43, 19, 65, 94, 3001, 535, 22, 42, 633, 317, 4397, 21, 141, 8, 74, 574, 214, 1286, 61, 253, 247, 1417, 163, 115, 217, 66, 546, 138, 10631, 1997, 51, 12097, 12301, 362, 26, 563, 1013

Offset

0,2

Links

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

Formula

a(n) = min { m >= 0 : A258851^3(m) = n }.

A258851^3(a(n)) = A258853(a(n)) = n.

a(n) <= A000040^3(n) for n>0.

a(n) <= A258861^3(n).

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(d(d(t)));
          if a(h) = -1 then a(h):= t fi
        od; a(n)
      end
    end():
seq(a(n), n=0..100);

Mathematica

d[n_] := d[n] = If[n == 0, 0, n*Total[Last[#]*PrimePi[First[#]]/First[#] & /@ FactorInteger[n]]];
A[n_, k_] := For[m = 0, True, m++, If[Nest[d, m, k] == n, Return[m]]];
a[n_] := A[n, 3];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, May 17 2024 *)

Crossrefs

Column k=3 of A259016.

Cf. A000040, A000720, A258851, A258853, A258861, A258862.

Sequence in context: A254766 A185201 A112956 * A335554 A157801 A061768

Adjacent sequences: A258992 A258993 A258994 * A258996 A258997 A258998

Keyword

nonn,changed

Author

Alois P. Heinz, Jun 16 2015

Status

approved