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Number of digits of Phi_n(10), or number of digits in base b of Phi_n(b), where Phi is the cyclotomic polynomial.
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%I #30 Dec 24 2014 23:32:47

%S 1,2,3,3,5,2,7,5,7,4,11,4,13,6,8,9,17,6,19,8,12,10,23,8,21,12,19,12,

%T 29,9,31,17,20,16,24,12,37,18,24,16,41,13,43,20,24,22,47,16,43,20,32,

%U 24,53,18,40,24,36,28,59,17,61,30,36,33,48,21,67,32,44,25,71,24

%N Number of digits of Phi_n(10), or number of digits in base b of Phi_n(b), where Phi is the cyclotomic polynomial.

%C a(n) = phi(n) if and only if the number of distinct prime factors of n (A001221(n)) is even, a(n) = phi(n) + 1 if and only if the number of distinct prime factors of n (A001221(n)) is odd, where phi is Euler's totient function.

%H Eric Chen, <a href="/A252502/b252502.txt">Table of n, a(n) for n = 1..1000</a>

%e Values of phi_n(b) written in base b are #, 11, 111, 101, 11111, #1, 1111111, 10001, 1001001, #0#1, 11111111111, ##01, ..., where # represents b - 1.

%t a252502[n_] := Array[Total@DigitCount[Cyclotomic[#, 10]] &, n]; a252502[72] (* _Michael De Vlieger_, Dec 21 2014 *)

%Y Cf. A000010, A019328, A063672, A206225.

%K nonn

%O 1,2

%A _Eric Chen_, Dec 17 2014