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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).
7
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, 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, 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
OFFSET
1,6
COMMENTS
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.
FORMULA
a(n) = A000005(n) - A324190(n).
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))));
A324191(n) = (numdiv(n)-A324190(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 19 2019
STATUS
approved