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A324190 Number of distinct values A297167 obtains over the divisors > 1 of n; a(1) = 0.

%I A324190 #17 Feb 19 2019 18:20:11
%S A324190 0,1,1,2,1,2,1,3,2,2,1,3,1,2,2,4,1,3,1,4,2,2,1,4,2,2,3,4,1,3,1,5,2,2,
%T A324190 2,4,1,2,2,5,1,3,1,4,3,2,1,5,2,3,2,4,1,4,2,6,2,2,1,4,1,2,4,6,2,3,1,4,
%U A324190 2,3,1,5,1,2,3,4,2,3,1,6,4,2,1,5,2,2,2,6,1,4,2,4,2,2,2,6,1,3,4,5,1,3,1,6,3
%N A324190 Number of distinct values A297167 obtains over the divisors > 1 of n; a(1) = 0.
%C A324190 Number of distinct values of the sum {excess of d} + {the index of the largest prime factor of d} (that is, A046660(d) + A061395(d)) that occurs over all divisors d > 1 of n.
%C A324190 Number of distinct values A297112 obtains over the divisors > 1 of n; a(1) = 0.
%H A324190 Antti Karttunen, <a href="/A324190/b324190.txt">Table of n, a(n) for n = 1..65537</a>
%H A324190 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A324190 a(n) = A001221(A324202(n)).
%F A324190 a(n) >= A324120(n).
%F A324190 a(n) >= A001222(n) >= A001221(n). [See A324179 and A324192 for differences]
%F A324190 a(n) <= A000005(n)-1. [See A324191 for differences]
%F A324190 For all primes p, a(p^k) = k.
%o A324190 (PARI)
%o A324190 A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
%o A324190 A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));
%o A324190 A324190(n) = #Set(apply(A297167, select(d -> d>1,divisors(n))));
%Y A324190 Cf. A000005, A001221, A001222, A046660, A061395, A324120, A324179, A324191, A324192, A324202, A324203.
%Y A324190 Cf. also A156552, A297112.
%K A324190 nonn
%O A324190 1,4
%A A324190 _Antti Karttunen_, Feb 19 2019