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A345220
Number of divisors of n with an even number of primes not exceeding them.
1
1, 1, 2, 2, 1, 2, 2, 3, 3, 2, 1, 3, 2, 3, 3, 4, 1, 3, 2, 4, 4, 2, 1, 4, 1, 2, 3, 4, 2, 5, 1, 4, 2, 1, 2, 4, 2, 3, 4, 6, 1, 5, 2, 4, 5, 2, 1, 5, 2, 2, 2, 3, 2, 4, 2, 6, 4, 3, 1, 7, 2, 2, 6, 5, 3, 4, 1, 2, 2, 4, 2, 6, 1, 2, 3, 4, 2, 4, 2, 8, 4, 2, 1, 6, 1, 2, 3, 5, 2, 8, 4, 4, 3
OFFSET
1,3
FORMULA
a(n) = Sum_{d|n} ((pi(d)+1) mod 2).
EXAMPLE
a(24) = 4; The divisors d of 24 are: 1, 2, 3, 4, 6, 8, 12, 24 and the corresponding values of pi(d) are: 0, 1, 2, 2, 3, 4, 5, 9. There are 4 even values of pi(d).
MATHEMATICA
Table[Sum[Mod[PrimePi[k] + 1, 2] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]
PROG
(PARI) a(n) = sumdiv(n, d, !(primepi(d) % 2)); \\ Michel Marcus, Jun 11 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 11 2021
STATUS
approved