cp's OEIS Frontend

A324191 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).

%I A324191 #13 Feb 19 2019 18:20:20
%S A324191 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 A324191 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 A324191 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 A324191 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 A324191 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 A324191 Antti Karttunen, <a href="/A324191/b324191.txt">Table of n, a(n) for n = 1..65537</a>
%H A324191 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A324191 a(n) = A000005(n) - A324190(n).
%o A324191 (PARI)
%o A324191 A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
%o A324191 A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));
%o A324191 A324190(n) = #Set(apply(A297167, select(d -> d>1,divisors(n))));
%o A324191 A324191(n) = (numdiv(n)-A324190(n));
%Y A324191 Cf. A000005, A001221, A001222, A046660, A061395, A297167, A324120, A324179, A324120, A324190, A324192.
%Y A324191 Cf. A000961 (positions of ones).
%K A324191 nonn
%O A324191 1,6
%A A324191 _Antti Karttunen_, Feb 19 2019