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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A351709 a(n) = Sum_{p|n, p prime} p!.

Original entry on oeis.org

0, 2, 6, 2, 120, 8, 5040, 2, 6, 122, 39916800, 8, 6227020800, 5042, 126, 2, 355687428096000, 8, 121645100408832000, 122, 5046, 39916802, 25852016738884976640000, 8, 120, 6227020802, 6, 5042, 8841761993739701954543616000000, 128, 8222838654177922817725562880000000
Offset: 1

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Author

Wesley Ivan Hurt, Feb 16 2022

Keywords

Comments

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

Examples

			a(6) = 8; a(6) = Sum_{p|6} p! = 2! + 3! = 2*1 + 3*2*1 = 8.

Crossrefs

Cf. A000040, A000142, A010051, A062363, A351708.

Formula

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

A351710 a(n) = Sum_{p|n, p prime} (n-p)!.

Original entry on oeis.org

0, 1, 1, 2, 1, 30, 1, 720, 720, 40440, 1, 3991680, 1, 479006640, 482630400, 87178291200, 1, 22230464256000, 1, 6403681380096000, 6402460884019200, 2432902008216556800, 1, 1175091669949317120000, 2432902008176640000, 620448401733245666380800, 620448401733239439360000
Offset: 1

Views

Author

Wesley Ivan Hurt, Feb 16 2022

Keywords

Examples

			a(6) = 30; a(6) = Sum_{p|6} (6-p)! = (6-2)! + (6-3)! = 4*3*2*1 + 3*2*1 = 30.

Crossrefs

Cf. A000040, A000142, A062363, A351708, A351709.

Formula

a(A000040(n)) = 1.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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