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

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, 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, 0, 93, 0, 152, 0, 19, 0, 46, 0, 111, 0, 30, 0, 99, 0, 170, 0, 19

Offset: 1

Author

Colin Defant, Apr 26 2014

Keywords

• nonn

Comments

It is interesting to note that a(37147) = 37147.

Also a(53290831) = 53290831. - Michel Marcus, Jun 18 2015

Examples

			A058026(7)=5, A058026(5)=3, A058026(3)=1, so a(7)=5+3+1=9. A058026(4)=0, so a(4)=0.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..40000
• Colin Defant, On Arithmetic Functions Related to Iterates of the Schemmel Totient Functions, arXiv:1506.05426 [math.NT], 2015.
• C. Defant, On Arithmetic Functions Related to Iterates of the Schemmel Totient Functions, J. Int. Seq. 18 (2015) # 15.2.1

Programs

Mathematica

L[n_, m_] :=
If[Min[Select[Divisors[n], PrimeQ]] <= m, 0,
  n*Times @@ (1 - m/(Select[Divisors[n], PrimeQ]))]
a[0] := 0
a[3] := 1
a[n_] := L[n, 2] + a[L[n, 2]]
Table[a[i], {i, 2, 30}]

PARI

a058026(n) = sumdiv(n, d, n/d*moebius(d)*numdiv(d));
a(n) = {s = 0; itn = n; while((itn) && (itn != 1), vb = a058026(itn); s += vb; itn = vb); s;} \\ Michel Marcus, May 21 2014