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

%I A258861 #21 Sep 10 2023 09:47:50
%S A258861 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,
%T A258861 26,21,103,107,109,25,34,16,18,139,38,151,33,163,167,173,35,181,191,
%U A258861 28,197,199,211,223,58,229,233,24,30,27,51,49,269,55,277,281,74
%N A258861 The pi-based antiderivative of n: the least m such that A258851(m) equals n.
%H A258861 Alois P. Heinz, <a href="/A258861/b258861.txt">Table of n, a(n) for n = 0..10000</a>
%F A258861 a(n) = min { m >= 0 : A258851(m) = n }.
%F A258861 A258851(a(n)) = n.
%F A258861 a(n) <= A000040(n) for n>0.
%p A258861 with(numtheory):
%p A258861 d:= n-> n*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]):
%p A258861 a:= proc() local t, a; t, a:= -1, proc() -1 end;
%p A258861       proc(n) local h;
%p A258861         while a(n) = -1 do
%p A258861           t:= t+1; h:= d(t);
%p A258861           if a(h) = -1 then a(h):= t fi
%p A258861         od; a(n)
%p A258861       end
%p A258861     end():
%p A258861 seq(a(n), n=0..100);
%t A258861 A258851[n_] := If[n == 0, 0, n*Total[Last[#]*PrimePi[First[#]]/First[#]& /@ FactorInteger[n]]];
%t A258861 a[n_] := For[m = 0, True, m++, If[A258851[m] == n, Return[m]]];
%t A258861 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Sep 10 2023 *)
%Y A258861 Column k=1 of A259016, A259153.
%Y A258861 Cf. A000040, A000720, A258851, A258862, A258995.
%K A258861 nonn
%O A258861 0,2
%A A258861 _Alois P. Heinz_, Jun 12 2015