A193453 Number of odd divisors of phi(n).

1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 2, 3, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 1, 4, 1, 2, 1, 2, 2, 3, 3, 2, 1, 2, 2, 4, 2, 2, 2, 2, 1, 4, 2, 1, 2, 2, 3, 2, 2, 3, 2, 2, 1, 4, 4, 3, 1, 2, 2, 4, 1, 2, 2, 4, 2, 3, 3, 2, 3, 4, 2, 4, 1, 4, 2, 2, 2, 1, 4, 2, 2, 2, 2, 3, 2, 4, 2, 3, 1, 2, 4, 4, 2, 3, 1, 4, 2, 2

Offset

1,7

Comments

phi(n) : A000010 is the Euler totient function. This sequence equals A193169 (n) for n < 63.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A001227(A000010(n)) = A000005(A053575(n)). - Antti Karttunen, Dec 04 2017

Example

a(63) = 3 because phi(63) = 36 with 3 odd divisors {1, 3, 9}.

Mathematica

f[n_] := Block[{d = Divisors[EulerPhi[n]]}, Count[OddQ[d], True]]; Table[f[n], {n, 80}]

Prog

(PARI) A193453(n) = sumdiv(eulerphi(n), d, d%2); \\ Antti Karttunen, Dec 04 2017

Crossrefs

Cf. A000010, A001227, A053575.

Sequence in context: A055734 A295660 A193169 * A227944 A095772 A305392

Adjacent sequences: A193450 A193451 A193452 * A193454 A193455 A193456

Keyword

nonn

Author

Michel Lagneau, Jul 26 2011

Extensions

More terms from Antti Karttunen, Dec 04 2017

Status

approved