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A241667 Sum of the iterates of A058026 up to and including either 0 or 1.

%I A241667 #34 Jan 27 2025 18:39:20
%S A241667 0,0,1,0,4,0,9,0,4,0,13,0,24,0,4,0,19,0,36,0,9,0,30,0,19,0,13,0,40,0,
%T A241667 69,0,13,0,19,0,54,0,24,0,63,0,104,0,13,0,58,0,54,0,19,0,70,0,40,0,36,
%U A241667 0,93,0,152,0,19,0,46,0,111,0,30,0,99,0,170,0,19
%N A241667 Sum of the iterates of A058026 up to and including either 0 or 1.
%C A241667 It is interesting to note that a(37147) = 37147.
%C A241667 Also a(53290831) = 53290831. - _Michel Marcus_, Jun 18 2015
%H A241667 Antti Karttunen, <a href="/A241667/b241667.txt">Table of n, a(n) for n = 1..40000</a>
%H A241667 Colin Defant, <a href="http://arxiv.org/abs/1506.05426">On Arithmetic Functions Related to Iterates of the Schemmel Totient Functions</a>, arXiv:1506.05426 [math.NT], 2015.
%H A241667 C. Defant, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Defant/defant5.html">On Arithmetic Functions Related to Iterates of the Schemmel Totient Functions</a>, J. Int. Seq. 18 (2015) # 15.2.1
%e A241667 A058026(7)=5, A058026(5)=3, A058026(3)=1, so a(7)=5+3+1=9. A058026(4)=0, so a(4)=0.
%t A241667 L[n_, m_] :=
%t A241667 If[Min[Select[Divisors[n], PrimeQ]] <= m, 0,
%t A241667   n*Times @@ (1 - m/(Select[Divisors[n], PrimeQ]))]
%t A241667 a[0] := 0
%t A241667 a[3] := 1
%t A241667 a[n_] := L[n, 2] + a[L[n, 2]]
%t A241667 Table[a[i], {i, 2, 30}]
%o A241667 (PARI) a058026(n) = sumdiv(n, d, n/d*moebius(d)*numdiv(d));
%o A241667 a(n) = {s = 0; itn = n; while((itn) && (itn != 1), vb = a058026(itn); s += vb; itn = vb); s;} \\ _Michel Marcus_, May 21 2014
%K A241667 nonn
%O A241667 1,5
%A A241667 _Colin Defant_, Apr 26 2014