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A053099
When the Euler phi function is iterated with initial value A002110(n) = n-th primorial, a(n) = exponent of largest power of 2 arising in the iteration.
2
1, 1, 3, 4, 7, 9, 13, 14, 18, 21, 24, 26, 31, 33, 38, 42, 46, 50, 54, 58, 61, 64, 70, 76, 81, 87, 92, 97, 99, 104, 106, 111, 118, 123, 127, 132, 136, 137, 144, 148, 155, 159, 163, 169, 173, 177, 181, 184, 190, 193, 199, 205, 211, 218, 226, 232, 238, 241, 247, 253
OFFSET
1,3
COMMENTS
Analogous to A053048.
LINKS
FORMULA
a(n) = log_2(A053098(n)). - Amiram Eldar, Nov 19 2024
EXAMPLE
For n = 6, A002110(6) = 30030, the corresponding iteration chain is {30030, 5760, 1536, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1}. The first power of 2 is the 4th item after 3 iterations. It is 512, therefore a(6) = log_2(512) = 9 and a(6) + 1 = 10 iterations is needed to reach the stationary value = 1.
MATHEMATICA
a[n_] := Max@ IntegerExponent[ FixedPointList[ EulerPhi, Times @@ Prime[ Range@ n]], 2]; Array[a, 60] (* Giovanni Resta, May 30 2018 *)
PROG
(PARI) a(n) = {my(p = prod(i=1, n, prime(i))); while(p >> valuation(p, 2) > 1, p = eulerphi(p)); valuation(p, 2); } \\ Amiram Eldar, Nov 19 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Feb 28 2000
STATUS
approved