A241668 Sum of iterates of A241663 up to and including either 0 or 1.

1, 0, 0, 0, 1, 0, 3, 0, 0, 0, 10, 0, 9, 0, 0, 0, 22, 0, 15, 0, 0, 0, 34, 0, 6, 0, 0, 0, 31, 0, 27, 0, 0, 0, 3, 0, 33, 0, 0, 0, 70, 0, 39, 0, 0, 0, 82, 0, 21, 0, 0, 0, 70, 0, 10, 0, 0, 0, 65, 0, 57, 0, 0, 0, 9, 0, 63, 0, 0, 0, 130, 0, 69, 0, 0, 0, 21, 0, 75, 0

Offset

1,7

Comments

This sequence is similar to the totient summatory function A092693, but uses the Schemmel totient function A241663 instead of the phi function.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

C. Defant, On Arithmetic Functions Related to Iterates of the Schemmel Totient Functions, J. Int. Seq. 18 (2015) # 15.2.1

Example

A241663(11)=7, A241663(7)=3, A241663(3)=0, so a(11)=7+3+0=10.
A241663(9)=0, so a(9)=0.

Mathematica

L[n_, m_] :=
If[Min[Select[Divisors[n], PrimeQ]] <= m, 0,
  n*Times @@ (1 - m/(Select[Divisors[n], PrimeQ]))]
a[0]:=0
a[5]:=1
a[n_]:=L[n, 4]+a[L[n, 4]]

Prog

(PARI)
A241663(n) = {my(f = factor(n)); prod(i=1, #f~, if ((f[i, 1] == 2) || (f[i, 1] == 3), 0, f[i, 1]^(f[i, 2]-1)*(f[i, 1]-4))); } \\ From A241663
A241668(n) = { my(s=(1==n)); while(n>1, n = A241663(n); s += n); (s); }; \\ Antti Karttunen, Oct 01 2018

Crossrefs

Cf. A092693, A241663, A241665.

Sequence in context: A370146 A325974 A057389 * A228861 A057382 A007270

Adjacent sequences: A241665 A241666 A241667 * A241669 A241670 A241671

Keyword

nonn

Author

Colin Defant, Apr 26 2014

Status

approved