A345045 -id:A345045 - 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).

A345044 If n = Product p(k)^e(k) then a(n) = LCM (p(k)^e(k) - 1).

Original entry on oeis.org

1, 1, 2, 3, 4, 2, 6, 7, 8, 4, 10, 6, 12, 6, 4, 15, 16, 8, 18, 12, 6, 10, 22, 14, 24, 12, 26, 6, 28, 4, 30, 31, 10, 16, 12, 24, 36, 18, 12, 28, 40, 6, 42, 30, 8, 22, 46, 30, 48, 24, 16, 12, 52, 26, 20, 42, 18, 28, 58, 12, 60, 30, 24, 63, 12, 10, 66, 48, 22, 12, 70, 56, 72, 36, 24, 18, 30, 12, 78, 60, 80, 40, 82, 6, 16, 42

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. A047994, A345045.

Cf. also A344878, A345046, A353783.

A345044(n) = { my(f=factor(n)~); lcm(vector(#f, i, (f[1, i]^f[2, i])-1)); };

a(n) = A047994(n) / A345045(n).

A345047 a(n) = A003958(n) / A345046(n), where A003958(n) is multiplicative with a(p^e) = (p-1)^e, and A345046(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, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 4, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 4, 1, 2, 1, 1, 4, 6, 1, 2, 1, 2, 1, 1, 1, 2, 1, 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. A003958, A345046.

Cf. also A345045, A353784.

A345047(n) = { my(f=factor(n)~, g=vector(#f, i, (f[1, i]-1)^f[2, i])); factorback(g)/lcm(g); };

a(n) = A003958(n) / A345046(n).

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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A345044 If n = Product p(k)^e(k) then a(n) = LCM (p(k)^e(k) - 1).

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A345047 a(n) = A003958(n) / A345046(n), where A003958(n) is multiplicative with a(p^e) = (p-1)^e, and A345046(n) gives the least common multiple of the same factors.

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