A053098 When the Euler phi function is iterated with initial value primorial(n) = A002110(n), a(n)= first (maximum) power of 2 emerging during iteration.
2, 2, 8, 16, 128, 512, 8192, 16384, 262144, 2097152, 16777216, 67108864, 2147483648, 8589934592, 274877906944, 4398046511104, 70368744177664, 1125899906842624, 18014398509481984, 288230376151711744, 2305843009213693952, 18446744073709551616, 1180591620717411303424
Offset: 1
Keywords
Examples
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) = 512.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..500
Programs
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Mathematica
a[n_] := 2^ Max@ IntegerExponent[ FixedPointList[ EulerPhi, Times @@ Prime[Range[n]]], 2]; Array[a, 20] (* Giovanni Resta, May 30 2018 *)
-
PARI
a(n) = {my(p = prod(i=1, n, prime(i))); while(p >> valuation(p, 2) > 1, p = eulerphi(p)); 1 << valuation(p, 2);} \\ Amiram Eldar, Nov 19 2024
Formula
a(n) = 2^A053099(n). - Amiram Eldar, Nov 19 2024
Extensions
a(21)-a(23) from Amiram Eldar, Nov 19 2024
Comments