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A324190
Number of distinct values A297167 obtains over the divisors > 1 of n; a(1) = 0.
10
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, 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, 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
OFFSET
1,4
COMMENTS
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.
Number of distinct values A297112 obtains over the divisors > 1 of n; a(1) = 0.
FORMULA
a(n) = A001221(A324202(n)).
a(n) >= A324120(n).
a(n) >= A001222(n) >= A001221(n). [See A324179 and A324192 for differences]
a(n) <= A000005(n)-1. [See A324191 for differences]
For all primes p, a(p^k) = k.
PROG
(PARI)
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));
A324190(n) = #Set(apply(A297167, select(d -> d>1, divisors(n))));
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 19 2019
STATUS
approved