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A071575 Number of iterations of cototient(n) needed to reach 1 (cototient(n) = n-phi(n)). 2
0, 1, 1, 2, 1, 3, 1, 3, 2, 4, 1, 4, 1, 4, 2, 4, 1, 5, 1, 5, 3, 5, 1, 5, 2, 5, 3, 5, 1, 6, 1, 5, 2, 6, 2, 6, 1, 6, 3, 6, 1, 7, 1, 6, 4, 6, 1, 6, 2, 7, 2, 6, 1, 7, 3, 6, 4, 7, 1, 7, 1, 6, 4, 6, 2, 7, 1, 7, 3, 7, 1, 7, 1, 7, 3, 7, 2, 8, 1, 7, 4, 8, 1, 8, 4, 7, 2, 7, 1, 8, 2, 7, 3, 7, 2, 7, 1, 7, 4, 8, 1, 8, 1, 7, 5, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
Paul Ellis, Jason Shi, Thotsaporn Aek Thanatipanonda, and Andrew Tu, Two Games on Arithmetic Functions: SALIQUANT and NONTOTIENT, arXiv:2309.01231 [math.NT], 2023. See p. 7.
FORMULA
a(n) = a(n-phi(n))+1, a(1) = 0.
a(n) = A076640(n)-1.
EXAMPLE
cototient(6) = 4, cototient(4) = 2, cototient(2) = 1, hence a(6) = 3.
MATHEMATICA
cot[n_] := n - EulerPhi[n]; a[n_] := -1 + Length @ NestWhileList[cot, n, # > 1 &]; Array[a, 100] (* Amiram Eldar, May 19 2022 *)
PROG
(PARI) for(n=1, 150, s=n; t=0; while(s!=1, t++; s=s-eulerphi(s); if(s==1, print1(t, ", "); ); ))
CROSSREFS
Sequence in context: A025808 A144079 A326839 * A307908 A366737 A316436
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, May 31 2002
EXTENSIONS
Prepended a(1)=0 and changed offset. - T. D. Noe, Dec 03 2008
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)