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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A158977 Product of the numbers k in the range 1 <= k <= n such that the proper divisors of k are a subset of the proper divisors of n.

Original entry on oeis.org

1, 2, 6, 24, 30, 720, 210, 6720, 1890, 8400, 2310, 47900160, 30030, 1681680, 4054050, 15375360, 510510, 1984862880, 9699690, 62078016000, 1833241410, 853572720, 223092870, 1776404640890880, 5577321750, 23201658480, 54211567410
Offset: 1

Views

Author

Jaroslav Krizek, Apr 01 2009

Keywords

Comments

Here, proper divisors include 1 but not the argument (k or n, respectively) in the divisor set, as counted in A032741.

Examples

			a(8) = 6720 is the product of the 7 numbers k: 1 {1}, 2 {1}, 3 {1}, 4 {1, 2}, 5 {1}, 7 {1}, 8 {1, 2, 4} with divisor set that are subsets of {1, 2, 4} for n = 8. 1 * 2 * 3 * 4 * 5 * 7 * 8 = 6720.

Crossrefs

Cf. A159073, A034386.

Programs

  • Magma
    [ &*[ k: k in [1..n] | forall(t){ d: d in Divisors(k) | d eq k or d in Divisors(n) } ]: n in [1..27] ]; // Klaus Brockhaus, Apr 07 2009

Formula

If p is prime, a(p) = A034386(p).
a(n)*A158978(n) = A000142(n). - R. J. Mathar, Apr 06 2009

Extensions

Edited by R. J. Mathar, Apr 06 2009
More terms from Klaus Brockhaus, Apr 07 2009

A159074 Sum of the k in the range 1<=k<=n such that set of proper divisors of k is not a subset of the set of proper divisors of n.

Original entry on oeis.org

1, 1, 1, 1, 5, 1, 11, 7, 19, 24, 38, 11, 50, 46, 55, 67, 95, 76, 113, 91, 124, 150, 176, 121, 200, 221, 242, 252, 306, 237
Offset: 1

Views

Author

Jaroslav Krizek, Apr 04 2009

Keywords

Comments

The nomenclature of A159072 applies, where the terms in that sum are counted.

Examples

			a(8) = 7 adds k = 6, where {1, 2, 3} is not a subset of the divisor set {1, 2, 4} of n = 8, and k = 1, with an empty proper divisor set.

Crossrefs

Cf.: A158976, A000217, A000040, A014284, A036234.

Formula

a(n) = A158976(n) + 1.
If p = prime, a(p) = A000217(p) - A158662(p) + 1 = A000217(p) - A014284[A036234(p)] + 1.
a(n)+A159073(n)=A000217(n). - R. J. Mathar, Apr 06 2009

Extensions

Edited by R. J. Mathar, Apr 06 2009
Showing 1-2 of 2 results.

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

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