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A258862 Second pi-based antiderivative of n: the least m such that A258851^2(m) equals n. 6

%I #17 Jun 19 2015 09:48:27

%S 0,3,5,11,4,10,41,13,15,83,109,29,19,35,191,43,30,277,74,14,8,42,77,

%T 431,461,21,22,563,66,599,26,78,12,61,141,163,877,18,214,218,226,38,

%U 114,201,105,1201,215,1297,302,55,1447,1471,89,25,103,170,58,291,51

%N Second pi-based antiderivative of n: the least m such that A258851^2(m) equals n.

%H Alois P. Heinz, <a href="/A258862/b258862.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = min { m >= 0 : A258851^2(m) = n }.

%F A258851^2(a(n)) = A258852(a(n)) = n.

%F a(n) <= A000040^2(n) for n>0.

%F a(n) <= A258861^2(n); a(21) = 42 < A258861^2(21) = A258861(22) = 79; A258851^2(42) = A258851^2(79) = 21.

%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(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);

%Y Column k=2 of A259016.

%Y Cf. A000040, A000720, A258851, A258852, A258861, A258995.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jun 12 2015

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)