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A370783
a(n) is the numerator of the sum of the reciprocals of the squarefree divisors of the powerful part of n.
2
1, 1, 1, 3, 1, 1, 1, 3, 4, 1, 1, 3, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 3, 6, 1, 4, 3, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 3, 4, 1, 1, 3, 8, 6, 1, 3, 1, 4, 1, 3, 1, 1, 1, 3, 1, 1, 4, 3, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 1, 3, 4, 1, 1, 3, 1, 1, 1
OFFSET
1,4
LINKS
FORMULA
a(n) = A332880(A057521(n)).
Let f(n) = a(n)/A370784(n):
f(n) is multiplicative with f(p) = 1 and f(p^e) = 1 + 1/p for e >= 2.
f(n) = 1 if and only if n is squarefree (A005117).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} f(k) = zeta(3)/zeta(6) = 1.181564... (A157289) (Jakimczuk, 2024).
EXAMPLE
Fractions begin with: 1, 1, 1, 3/2, 1, 1, 1, 3/2, 4/3, 1, 1, 3/2, ...
MATHEMATICA
a[n_] := Numerator[Times @@ (1 + 1/Select[FactorInteger[n], Last[#] > 1 &][[;; , 1]])]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); numerator(prod(i = 1, #f~, if(f[i, 2] == 1, 1, 1 + 1/f[i, 1]))); }
CROSSREFS
Cf. A005117, A057521, A157289, A295295, A332880, A370784 (denominators).
Sequence in context: A351149 A191523 A132890 * A295295 A365336 A365404
KEYWORD
nonn,easy,frac
AUTHOR
Amiram Eldar, Mar 02 2024
STATUS
approved