cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A351750 a(n) = Sum_{p|n, p prime} p * sigma_p(p).

Original entry on oeis.org

0, 10, 84, 10, 15630, 94, 5764808, 10, 84, 15640, 3138428376732, 94, 3937376385699302, 5764818, 15714, 10, 14063084452067724991026, 94, 37589973457545958193355620, 15640, 5764892, 3138428376742, 480250763996501976790165756943064, 94, 15630, 3937376385699312
Offset: 1

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Author

Wesley Ivan Hurt, Feb 17 2022

Keywords

Comments

Inverse Möbius transform of n * sigma_n(n) * c(n), where c(n) is the characteristic function of primes (A010051). - Wesley Ivan Hurt, Apr 01 2025

Examples

			a(6) = 94; a(6) = Sum_{p|6, p prime} p * sigma_p(p) = 2 * sigma_2(2) + 3 * sigma_3(3) = 2 * (1^2 + 2^2) + 3 * (1^3 + 3^3) = 94.

Crossrefs

Cf. A010051, A023887 (sigma_n(n)), A351749.

Formula

a(n) = Sum_{d|n} d * sigma_d(d) * c(d), where c = A010051. - Wesley Ivan Hurt, Apr 01 2025

A351751 a(n) = Sum_{p|n, p prime} p^sigma_p(p).

Original entry on oeis.org

0, 32, 22876792454961, 32
Offset: 1

Views

Author

Wesley Ivan Hurt, Feb 17 2022

Keywords

Comments

a(5) has 2185 digits.
Inverse Möbius transform of n^sigma_n(n) * c(n), where c(n) is the characteristic function of primes (A010051). - Wesley Ivan Hurt, Apr 01 2025

Examples

			a(3) = 22876792454961; a(3) = Sum_{p|3, p prime} p^sigma_p(p) = 3^(1^3 + 3^3) = 3^28 = 22876792454961.

Crossrefs

Cf. A010051, A023887 (sigma_n(n)), A351749.

Formula

a(n) = Sum_{d|n} d^sigma_d(d) * c(d), where c = A010051. - Wesley Ivan Hurt, Apr 01 2025
Showing 1-2 of 2 results.

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