A324650 a(n) = A000010(A276086(n)).

1, 1, 2, 2, 6, 6, 4, 4, 8, 8, 24, 24, 20, 20, 40, 40, 120, 120, 100, 100, 200, 200, 600, 600, 500, 500, 1000, 1000, 3000, 3000, 6, 6, 12, 12, 36, 36, 24, 24, 48, 48, 144, 144, 120, 120, 240, 240, 720, 720, 600, 600, 1200, 1200, 3600, 3600, 3000, 3000, 6000, 6000, 18000, 18000, 42, 42, 84, 84, 252, 252, 168, 168, 336, 336, 1008, 1008

Offset: 0

Author

Antti Karttunen, Mar 10 2019

Keywords

• nonn

Comments

Terms are duplicated because phi(2*(2n+1)) = phi(2n+1) for all n >= 0.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..2310
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A000010, A002110, A276086, A324651 (bisection).

Cf. also A267263, A276150, A324653, A324655 for omega, bigomega, sigma and tau analogs.

Cf. also A290077.

Programs

PARI

A324650(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr), m *= (prime(i)-1)*(prime(i)^(((n%nextpr)/pr)-1)); n-=(n%nextpr));pr=nextpr); (m); };

PARI

A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
A324650(n) = eulerphi(A276086(n));

Formula

a(n) = A000010(A276086(n)).

a(2n+1) = a(2n) for all n >= 0.

For n >= 1, a(A002110(n-1)) = A000040(n)-1.