A370784 a(n) is the denominator of the sum of the reciprocals of the squarefree divisors of the powerful part of n.

1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 5, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 7, 5, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 5, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Rafael Jakimczuk, Arithmetical Functions over the Powerful Part of an Integer, ResearchGate, 2024.

Formula

a(n) = A332881(A057521(n)).

a(n) = 1 if n is squarefree (A005117).

Mathematica

a[n_] := Denominator[Times @@ (1 + 1/Select[FactorInteger[n], Last[#] > 1 &][[;; , 1]])]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n)); denominator(prod(i = 1, #f~, if(f[i, 2] == 1, 1, 1 + 1/f[i, 1]))); }

Crossrefs

Cf. A005117, A057521, A295295, A332881, A370783 (numerators).

Sequence in context: A228349 A285718 A205792 * A249739 A249740 A071773

Adjacent sequences: A370781 A370782 A370783 * A370785 A370786 A370787

Keyword

nonn,easy,frac

Author

Amiram Eldar, Mar 02 2024

Status

approved