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A324650 a(n) = A000010(A276086(n)). 12

%I #11 Mar 10 2019 19:32:12

%S 1,1,2,2,6,6,4,4,8,8,24,24,20,20,40,40,120,120,100,100,200,200,600,

%T 600,500,500,1000,1000,3000,3000,6,6,12,12,36,36,24,24,48,48,144,144,

%U 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

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

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

%H Antti Karttunen, <a href="/A324650/b324650.txt">Table of n, a(n) for n = 0..2310</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

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

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

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

%o (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); };

%o (PARI)

%o 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; };

%o A324650(n) = eulerphi(A276086(n));

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

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

%Y Cf. also A290077.

%K nonn

%O 0,3

%A _Antti Karttunen_, Mar 10 2019

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Last modified April 24 22:17 EDT 2024. Contains 371964 sequences. (Running on oeis4.)