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Number of common divisors of n and A276086(n), with a(0) = 1.
4

%I #7 Sep 19 2019 21:13:40

%S 1,1,1,2,1,1,1,1,1,2,2,1,1,1,1,4,1,1,1,1,2,2,1,1,1,3,1,2,1,1,1,1,1,2,

%T 1,2,1,1,1,2,2,1,2,1,1,4,1,1,1,2,3,2,1,1,1,2,2,2,1,1,1,1,1,4,1,1,1,1,

%U 1,2,4,1,1,1,1,6,1,2,1,1,2,2,1,1,2,2,1,2,1,1,1,2,1,2,1,1,1,1,3,2,2,1,1,1,1,8

%N Number of common divisors of n and A276086(n), with a(0) = 1.

%H Antti Karttunen, <a href="/A327168/b327168.txt">Table of n, a(n) for n = 0..16383</a>

%H Antti Karttunen, <a href="/A327168/a327168.txt">Data supplement: n, a(n) computed for n = 0..65537</a>

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

%F a(n) = A000005(A324198(n)).

%F a(n) = 1+A001222(A327167(n)) for n >= 1.

%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 A327168(n) = numdiv(gcd(n,A276086(n)));

%Y Cf. A000005, A001222, A276086, A324198, A327167.

%Y Cf. also A323878.

%K nonn

%O 0,4

%A _Antti Karttunen_, Sep 19 2019