A353381 - OEIS

%I #7 Apr 19 2022 22:45:20

%S 0,1,1,1,1,2,1,1,1,3,1,2,1,2,2,2,1,2,1,3,3,3,1,3,1,2,1,2,1,5,1,2,2,3,

%T 2,2,1,2,3,4,1,5,1,3,2,3,1,4,1,3,2,2,1,3,3,3,3,2,1,5,1,3,3,2,2,5,1,3,

%U 2,5,1,3,1,2,2,2,2,5,1,6,2,3,1,5,3,2,3,4,1,5,3,3,2,3,2,4,1,2,2,3,1,5,1,3,5

%N Number of divisors of n not in A353355.

%H Antti Karttunen, <a href="/A353381/b353381.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) = Sum_{d|n} 1-A353380(d).

%F a(n) = A000005(n) - A353382(n).

%F a(p) = 1 for all primes p.

%F a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.

%o (PARI)

%o A332823(n) = { my(f = factor(n),u=(sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2)%3); if(2==u,-1,u); };

%o A353354(n) = sumdiv(n,d,A332823(d));

%o A353380(n) = (0==A353354(n));

%o A353381(n) = sumdiv(n,d,!A353380(d));

%Y Cf. A000005, A003961, A048675, A332823, A348717, A353352, A353354, A353355, A353380, A353382.

%K nonn

%O 1,6

%A _Antti Karttunen_, Apr 19 2022