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Number of distinct values A297167 obtains over divisors > 1 of n, minus number of distinct prime factors of n: a(n) = A324190(n) - A001221(n).
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%I #7 Feb 19 2019 18:20:26

%S 0,0,0,1,0,0,0,2,1,0,0,1,0,0,0,3,0,1,0,2,0,0,0,2,1,0,2,2,0,0,0,4,0,0,

%T 0,2,0,0,0,3,0,0,0,2,1,0,0,3,1,1,0,2,0,2,0,4,0,0,0,1,0,0,2,5,0,0,0,2,

%U 0,0,0,3,0,0,1,2,0,0,0,4,3,0,0,2,0,0,0,4,0,1,0,2,0,0,0,4,0,1,2,3,0,0,0,4,0

%N Number of distinct values A297167 obtains over divisors > 1 of n, minus number of distinct prime factors of n: a(n) = A324190(n) - A001221(n).

%H Antti Karttunen, <a href="/A324192/b324192.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) = A324190(n) - A001221(n).

%F a(n) >= A324179(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 A324192(n) = (A324190(n)-omega(n));

%Y Cf. A001222, A324179.

%K nonn

%O 1,8

%A _Antti Karttunen_, Feb 19 2019