A329036 - OEIS

%I #6 Nov 08 2019 18:16:09

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

%T 1,2,1,2,2,3,1,4,1,3,2,2,1,2,1,2,2,3,1,1,1,8,2,2,1,4,1,2,1,1,1,4,1,3,

%U 2,4,1,2,1,2,6,3,1,4,1,3,1,2,1,12,1,2,2,4,1,4,1,3,2,2,1,2,1,1,1,1,1,4,1,4,4

%N Number of common divisors of n and A122111(n).

%H Antti Karttunen, <a href="/A329036/b329036.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A000005(A280491(n)) = A000005(gcd(n, A122111(n))).

%F a(n) = 1+A001222(A329042(n)) = 1+A001222(A329043(n)).

%o (PARI)

%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};

%o A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));

%o A280491(n) = gcd(n,A122111(n));

%o A329036(n) = numdiv(A280491(n));

%Y Cf. A000005, A001222, A122111, A280491, A329042, A329043.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 08 2019