A345047 -id:A345047 - cp's OEIS frontend

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

Antti Karttunen, May 08 2022

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sigma(n)

Cf. A000203, A353783.
Cf. A336547 (positions of 1's), A336548 (of terms > 1).
Cf. also A345045, A345047

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

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

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

A345045 a(n) = A047994(n) / A345044(n), where A047994(n) is multiplicative with a(p^e) = p^e - 1, and A345044(n) gives the least common multiple of the same factors.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jun 07 2021

nonn

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

Cf. A047994, A345044.

Cf. also A344879, A345047, A353784.

A345045(n) = { my(f=factor(n)~, g=vector(#f, i, (f[1, i]^f[2, i])-1)); factorback(g)/lcm(g); };

a(n) = A047994(n) / A345044(n).

A345046 If n = Product p(k)^e(k) then a(n) = LCM (p(k)-1)^e(k).

Original entry on oeis.org

1, 1, 2, 1, 4, 2, 6, 1, 4, 4, 10, 2, 12, 6, 4, 1, 16, 4, 18, 4, 6, 10, 22, 2, 16, 12, 8, 6, 28, 4, 30, 1, 10, 16, 12, 4, 36, 18, 12, 4, 40, 6, 42, 10, 4, 22, 46, 2, 36, 16, 16, 12, 52, 8, 20, 6, 18, 28, 58, 4, 60, 30, 12, 1, 12, 10, 66, 16, 22, 12, 70, 4, 72, 36, 16, 18, 30, 12, 78, 4, 16, 40, 82, 6, 16, 42, 28, 10

Offset: 1

Antti Karttunen, Jun 07 2021

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to lcm's

Cf. A003958, A345047.

Cf. also A345044, A353783.

A345046(n) = { my(f=factor(n)~); lcm(vector(#f, i, (f[1, i]-1)^f[2, i])); };

cp's OEIS Frontend

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.

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Formula

A345045 a(n) = A047994(n) / A345044(n), where A047994(n) is multiplicative with a(p^e) = p^e - 1, and A345044(n) gives the least common multiple of the same factors.

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Author

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Links

Crossrefs

Programs

PARI

Formula

A345046 If n = Product p(k)^e(k) then a(n) = LCM (p(k)-1)^e(k).

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Author

Keywords

Links

Crossrefs

Programs

PARI