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A258862
Second pi-based antiderivative of n: the least m such that A258851^2(m) equals n.
6
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
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);
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, 2];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, May 17 2024 *)
CROSSREFS
Column k=2 of A259016.
Sequence in context: A365443 A268034 A286567 * A139430 A143386 A214862
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 12 2015
STATUS
approved