A252502 Number of digits of Phi_n(10), or number of digits in base b of Phi_n(b), where Phi is the cyclotomic polynomial.

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, 29, 9, 31, 17, 20, 16, 24, 12, 37, 18, 24, 16, 41, 13, 43, 20, 24, 22, 47, 16, 43, 20, 32, 24, 53, 18, 40, 24, 36, 28, 59, 17, 61, 30, 36, 33, 48, 21, 67, 32, 44, 25, 71, 24

Offset

1,2

Comments

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.

Links

Eric Chen, Table of n, a(n) for n = 1..1000

Example

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.

Mathematica

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

Crossrefs

Cf. A000010, A019328, A063672, A206225.

Sequence in context: A069461 A329071 A232932 * A063256 A229703 A348883

Adjacent sequences: A252499 A252500 A252501 * A252503 A252504 A252505

Keyword

nonn

Author

Eric Chen, Dec 17 2014

Status

approved