A389075 Denominator of ratio A034448(n) / A048250(n), where A034448 is the sum of unitary divisors and A048250 is the sum of squarefree divisors.

1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 3, 1, 2, 1, 3, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 3, 4, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 3, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 1, 3, 2, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 4, 2, 9, 1, 1, 1, 1, 1

Offset

1,4

Comments

See comments in A389074.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = A048250(n) / A323159(n).

Mathematica

A389075[n_] := Denominator[Times @@ (Power @@@ # + 1)/Times @@ (#[[All, 1]] + 1)] & [FactorInteger[n]];
Array[A389075, 100]  (* Paolo Xausa, Oct 07 2025 *)

Prog

(PARI)
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); };
A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));
A389075(n) = denominator(A034448(n)/A048250(n));

Crossrefs

Cf. A034448, A048250, A323159, A389074 (numerators).

Cf. also A348734, A348735.

Sequence in context: A353784 A117544 A030393 * A328391 A109393 A030348

Adjacent sequences: A389072 A389073 A389074 * A389076 A389077 A389078

Keyword

nonn,frac

Author

Antti Karttunen, Sep 30 2025

Status

approved