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A156776 Number of iterations of x->(sigma(x)+phi(x))/2 until a non-integer is reached when starting with x=n; a(n)=0 if this never happens. 2
0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0, 3, 2, 1, 0, 1, 0, 2, 0, 0, 0, 4, 1, 0, 0, 4, 0, 0, 0, 1, 4, 3, 2, 1, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 7, 1, 1, 0, 0, 0, 8, 3, 2, 0, 0, 0, 0, 0, 8, 7, 1, 0, 0, 0, 0, 7, 6, 0, 1, 0, 0, 0, 4, 6, 5, 0, 0, 1, 0, 0, 5, 6, 5, 4, 3, 0, 9, 0, 0, 7, 6, 5, 4, 0, 1, 9, 1, 0, 5, 0, 9, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

In [Guy 1997] the iteration is said to fracture when sigma(x)+phi(x) becomes odd. For n with a(n)=0, A156775(n) gives the number of iterations until a previously seen term is encountered.

LINKS

Table of n, a(n) for n=1..105.

Richard K. Guy, Divisors and desires, Amer. Math. Monthly, 104 (1997), 359-360.

EXAMPLE

Let f(x)=(sigma(x)+phi(x))/2. For x=1 we have f(x) = (1+1)/2 = 1, i.e. this is a fixed point and the sequence will never fraction, hence a(1)=0. The same happens for x=2, x=3 and x=5. For x=4 we have f(x) = (7+2)/2 = 9/2, the sequence "fractures" after a(4)=1 iterations. For x=6 we have f(x) = (12+2)/2 = 7, f(7) = (8+6)/2 = 7, a fixed point, so again a(6)=a(7)=0.

PROG

(PARI) A156776(n, u=[])={ until( denominator( n=(sigma(n)+eulerphi(n))/2)>1 | setsearch(u, n), u=setunion(u, Set(n))); if( denominator(n)>1, #u) }

CROSSREFS

Cf. A065387(n) = A000203(n) + A000010(n).

Sequence in context: A154752 A271868 A194354 * A292108 A325195 A026728

Adjacent sequences:  A156773 A156774 A156775 * A156777 A156778 A156779

KEYWORD

nonn

AUTHOR

M. F. Hasler, Feb 15 2009

STATUS

approved

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Last modified July 2 09:21 EDT 2020. Contains 335398 sequences. (Running on oeis4.)