A258995 - OEIS

%I #11 May 18 2024 01:54:38

%S 0,5,11,10,4,29,35,41,14,431,599,78,15,38,201,191,25,382,186,43,19,65,

%T 94,3001,535,22,42,633,317,4397,21,141,8,74,574,214,1286,61,253,247,

%U 1417,163,115,217,66,546,138,10631,1997,51,12097,12301,362,26,563,1013

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

%H Alois P. Heinz, <a href="/A258995/b258995.txt">Table of n, a(n) for n = 0..10000</a>

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

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

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

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

%p with(numtheory):

%p d:= n-> n*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]):

%p a:= proc() local t, a; t, a:= -1, proc() -1 end;

%p       proc(n) local h;

%p         while a(n) = -1 do

%p           t:= t+1; h:= d(d(d(t)));

%p           if a(h) = -1 then a(h):= t fi

%p         od; a(n)

%p       end

%p     end():

%p seq(a(n), n=0..100);

%t d[n_] := d[n] = If[n == 0, 0, n*Total[Last[#]*PrimePi[First[#]]/First[#] & /@ FactorInteger[n]]];

%t A[n_, k_] := For[m = 0, True, m++, If[Nest[d, m, k] == n, Return[m]]];

%t a[n_] := A[n, 3];

%t Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, May 17 2024 *)

%Y Column k=3 of A259016.

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

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jun 16 2015