A324191 - OEIS

%I #13 Feb 19 2019 18:20:20

%S 1,1,1,1,1,2,1,1,1,2,1,3,1,2,2,1,1,3,1,2,2,2,1,4,1,2,1,2,1,5,1,1,2,2,

%T 2,5,1,2,2,3,1,5,1,2,3,2,1,5,1,3,2,2,1,4,2,2,2,2,1,8,1,2,2,1,2,5,1,2,

%U 2,5,1,7,1,2,3,2,2,5,1,4,1,2,1,7,2,2,2,2,1,8,2,2,2,2,2,6,1,3,2,4,1,5,1,2,5

%N Number of divisors of n minus the number of distinct values that A297167 obtains over the divisors > 1 of n: a(n) = A000005(n) - A324190(n).

%C a(p^k) = 1 for all primes p and all exponents k >= 0, because with prime powers there are k divisors larger than 1 and A297167 obtains a distinct value for each one of them.

%H Antti Karttunen, <a href="/A324191/b324191.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(n) - A324190(n).

%o (PARI)

%o A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));

%o A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));

%o A324190(n) = #Set(apply(A297167, select(d -> d>1,divisors(n))));

%o A324191(n) = (numdiv(n)-A324190(n));

%Y Cf. A000005, A001221, A001222, A046660, A061395, A297167, A324120, A324179, A324120, A324190, A324192.

%Y Cf. A000961 (positions of ones).

%K nonn

%O 1,6

%A _Antti Karttunen_, Feb 19 2019