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A366991
The number of divisors of n that are not terms of A322448.
4
1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 4, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 5, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 2, 8, 3, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 12, 2, 4, 6, 5, 4, 8, 2, 6, 4, 8, 2, 12, 2, 4, 6, 6, 4, 8, 2, 8, 4, 4, 2, 12, 4, 4
OFFSET
1,2
COMMENTS
First differs from A365680 at n = 64.
The number of divisors of n whose prime factorization has exponents that are all either 1 or primes.
The sum of these divisors is A366992(n) and the largest of them is A366994(n).
LINKS
FORMULA
Multiplicative with a(p^e) = A000720(e) + 2.
a(n) <= A000005(n), with equality if and only if n is a biquadratefree number (A046100).
MATHEMATICA
f[p_, e_] := PrimePi[e] + 2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, primepi(f[i, 2]) + 2); }
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Oct 31 2023
STATUS
approved