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

0, 3, 5, 11, 4, 10, 41, 13, 15, 83, 109, 29, 19, 35, 191, 43, 30, 277, 74, 14, 8, 42, 77, 431, 461, 21, 22, 563, 66, 599, 26, 78, 12, 61, 141, 163, 877, 18, 214, 218, 226, 38, 114, 201, 105, 1201, 215, 1297, 302, 55, 1447, 1471, 89, 25, 103, 170, 58, 291, 51

Offset

0,2

Links

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

Formula

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

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

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

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

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

Crossrefs

Column k=2 of A259016.

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

Sequence in context: A365443 A268034 A286567 * A139430 A143386 A214862

Adjacent sequences: A258859 A258860 A258861 * A258863 A258864 A258865

Keyword

nonn

Author

Alois P. Heinz, Jun 12 2015

Status

approved