A128853 a(n) is the number of positive divisors of n which are coprime to phi(n) = A000010(n).

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

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Example

12 is coprime to 4 positive integers (1,5,7 and 11) which are <= 12; so phi(12)=4. There are 2 divisors (1 and 3) of 12 that are coprime to 4. So a(12) = 2.

Maple

with(numtheory): a:=proc(n) local div, ct, j: div:=divisors(n): ct:=0: for j from 1 to tau(n) do if igcd(div[j], phi(n))=1 then ct:=ct+1 else fi od: ct; end: seq(a(n), n=1..140); # Emeric Deutsch, Apr 17 2007

Mathematica

Table[Total[Boole[CoprimeQ[Divisors[n], EulerPhi[n]]]], {n, 120}] (* Harvey P. Dale, Oct 18 2020 *)

Prog

(PARI) A128853(n) = { my(ph=eulerphi(n)); sumdiv(n, d, (1==(gcd(d, ph)))); }; \\ Antti Karttunen, Sep 27 2018

Crossrefs

Sequence in context: A214517 A230594 A072463 * A136165 A134193 A230259

Adjacent sequences: A128850 A128851 A128852 * A128854 A128855 A128856

Keyword

nonn

Author

Leroy Quet, Apr 16 2007

Extensions

More terms from Emeric Deutsch, Apr 17 2007

Status

approved