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.

Showing 1-2 of 2 results.

A159073 Sum of the k in the range 1

Original entry on oeis.org

0, 2, 5, 9, 10, 20, 17, 29, 26, 31, 28, 67, 41, 59, 65, 69, 58, 95, 77, 119, 107, 103, 100, 179, 125, 130, 136, 154, 129, 228, 160, 220, 202, 198, 220, 280, 197, 239, 245, 320, 238, 334, 281, 359, 402, 331, 328, 487, 377, 417, 388, 418, 381, 499, 461, 556, 447, 443, 440
Offset: 1

Views

Author

Jaroslav Krizek, Apr 04 2009

Keywords

Comments

Here proper divisors include 1 but not the argument (k or n, respectively) in the divisor set, as defined in A032741.
Terms of the sum are counted in A159070.

Examples

			a(8) = 29 is the sum of the following six k: 2 {1}, 3 {1}, 4 {1, 2}, 5 {1}, 7 {1}, 8 {1, 2, 4} with subsets of the proper divisors {1, 2, 4} of n = 8. 2 + 3 + 4 + 5 + 7 + 8 = 29.

Crossrefs

Cf.: A158975, A000040, A014284, A036234.

Formula

a(n) = A158975(n) - 1.
If p = prime, element of A000040, a(p) = A158662(p) - 1 = A014284(A036234(p)) - 1.

Extensions

Edited and extended by R. J. Mathar, Apr 06 2009

A159072 Count of numbers k in the range 1<=k<= n such that set of proper divisors of k is not a subset of the set of the proper divisors of n.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 3, 2, 4, 4, 6, 2, 7, 6, 7, 7, 10, 7, 11, 8, 11, 12, 14, 8, 15, 15, 16, 15, 19, 13, 20, 17, 20, 21, 22, 17, 25, 24, 25, 21, 28, 23, 29, 26, 26, 30, 32, 24, 33, 31, 34, 33, 37, 32, 37, 33, 39, 40, 42, 32, 43, 42, 40, 41, 45, 42, 48, 45, 48, 44, 51, 41, 52, 51, 50, 51, 54
Offset: 1

Views

Author

Jaroslav Krizek, Apr 04 2009

Keywords

Comments

Here proper divisors include 1 but not the argument (k or n, respectively) in the divisor set, as defined in A032741.
We use the (nonstandard) terminology that the empty set (the proper divisors of 1) is not a subset of another set.

Examples

			a(8) = 2 counts k=6 with divisors set {1, 2, 3} (not subset of the divisors {1, 2, 4} of n = 8), and k=1 without proper divisors.

Crossrefs

Cf.: A158974, A000040, A036234, A000720.

Formula

a(n)+A159070(n) = n. - R. J. Mathar, Apr 06 2009

Extensions

Edited and extended 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.

Content is available under The OEIS End-User License Agreement.