A353784 a(n) = sigma(n) / LCM_{p^e||n} sigma(p^e), where n = Product_{p^e||n}, with each p^e the maximal power of prime p that divides n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 3, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 4, 3, 2, 1, 1, 1, 2, 3, 1, 4, 1, 1, 1, 3, 1, 1, 1, 1, 2, 7, 1, 1, 6, 1, 4, 3, 1, 2, 1, 1, 1, 1, 2, 12, 1, 1, 4, 6, 1, 1, 1, 1, 1, 1, 4, 2, 1, 1, 1, 3, 1, 4, 6, 1, 2, 3, 1, 3, 2, 1, 4, 3, 2, 1, 1, 3, 1, 1, 1, 6, 1, 1, 8

Offset

1,10

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sigma(n)

Formula

a(n) = A000203(n) / A353783(n).

Mathematica

Array[DivisorSigma[1, #]/(LCM @@ DivisorSigma[1, Power @@@ FactorInteger[#]]) &, 105] (* Michael De Vlieger, May 08 2022 *)

Prog

(PARI) A353784(n) = { my(f=factor(n)~); (sigma(n) / lcm(vector(#f, i, sigma(f[1, i]^f[2, i])))); };

Crossrefs

Cf. A000203, A353783.

Cf. A336547 (positions of 1's), A336548 (of terms > 1).

Cf. also A345045, A345047

Sequence in context: A051714 A023593 A353755 * A117544 A030393 A328391

Adjacent sequences: A353781 A353782 A353783 * A353785 A353786 A353787

Keyword

nonn

Author

Antti Karttunen, May 08 2022

Status

approved