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 1-4 of 4 results.

A090055 Numbers n divisible by at least one nontrivial permutation (rearrangement) of the digits of n.

Original entry on oeis.org

105, 108, 405, 510, 540, 702, 703, 810, 1001, 1005, 1008, 1020, 1050, 1053, 1080, 2002, 2016, 2025, 2040, 2050, 2079, 2100, 2106, 3003, 3024, 3042, 3045, 3060, 3105, 3402, 3510, 4004, 4005, 4050, 4070, 4080, 4200, 5005, 5010, 5040
Offset: 1

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Author

Chuck Seggelin, Nov 21 2003

Keywords

Comments

Trivial permutations are identified as (1) permutation = n, or (2) when n mod 10=0, permutations of n's digits which result in shifting only trailing zeros to the most significant side of n where they drop off, such that permutation = n/10^z, where z <= the number of trailing zeros of n. So if n were 1809000, the following permutations would be excluded as trivial: 1809000, 0180900, 0018090, 0001809.
A031877 (numbers which are multiples of their reversals) and both A084687 and A090053 (numbers divided by number formed by sorting their digits), are subsets of this sequence. This sequence differentiates itself by including terms such as 7425 which is divided by 2475 (a rearrangement of 7425's digits that is neither a reversal or an ascending sort.)

Examples

			a(27)=3045 because 3045 is divisible by 435, a nontrivial permutation of 3045. (0435)

Links

Crossrefs

Cf. A031877, A084687, A090056, A090057, A090058, A090059, A090060.

A090057 Numbers n divisible by exactly two nontrivial permutations (rearrangements) of the digits of n.

Original entry on oeis.org

1050, 1080, 3105, 5100, 5400, 7020, 7030, 9207, 9801, 10010, 10050, 10080, 10098, 10200, 10206, 20020, 20160, 20250, 20304, 20400, 20500, 20790, 21000, 21060, 30015, 30030, 30105, 30240, 30420, 30450, 30600, 35100, 40040, 40050
Offset: 1

Views

Author

Chuck Seggelin, Nov 21 2003

Keywords

Comments

Trivial permutations are identified as (1) permutation = n, or (2) when n mod 10=0, permutations of n's digits which result in shifting only trailing zeros to the most significant side of n where they drop off, such that permutation = n/10^z, where z <= the number of trailing zeros of n. So if n were 1809000, the following permutations would be excluded as trivial: 1809000, 0180900, 0018090, 0001809.

Examples

			a(3)=3105 because 3105 is divisible by both 135 and 1035, two nontrivial permutations of 3105. a(8)=9207 because 9207 is divisible by both 279 and 297, two nontrivial permutations of 9207.

Links

Crossrefs

Cf. A090055, A090058, A090059, A090060, A090061.

A090058 Numbers n divisible by exactly three nontrivial permutations (rearrangements) of the digits of n.

Original entry on oeis.org

4050, 8100, 10500, 10530, 10800, 34020, 51000, 54000, 60912, 68040, 70300, 80190, 95040, 100100, 100500, 100800, 102000, 105030
Offset: 1

Views

Author

Chuck Seggelin, Nov 21 2003

Keywords

Comments

Trivial permutations are identified as (1) permutation = n, or (2) when n mod 10=0, permutations of n's digits which result in shifting only trailing zeros to the most significant side of n where they drop off, such that permutation = n/10^z, where z <= the number of trailing zeros of n. So if n were 1809000, the following permutations would be excluded as trivial: 1809000, 0180900, 0018090, 0001809.

Examples

			60912 is a term because 60912 is divisible by 1269, 1296 and 1692, three nontrivial permutations of 60912.

Links

Crossrefs

Cf. A090055, A090057, A090059, A090060, A090061.

A090059 Numbers n divisible by exactly four nontrivial permutations (rearrangements) of the digits of n.

Original entry on oeis.org

31050, 50490, 70200, 92070, 100035, 100980, 102060, 105000, 108000
Offset: 1

Views

Author

Chuck Seggelin, Nov 21 2003

Keywords

Comments

Trivial permutations are identified as (1) permutation = n, or (2) when n mod 10=0, permutations of n's digits which result in shifting only trailing zeros to the most significant side of n where they drop off, such that permutation = n/10^z, where z <= the number of trailing zeros of n. So if n were 1809000, the following permutations would be excluded as trivial: 1809000, 0180900, 0018090, 0001809.

Examples

			50490 is a term because 50490 is divisible by 459, 495, 594 and 4590, four nontrivial permutations of 50490.

Links

Crossrefs

Cf. A090055, A090057, A090058, A090060, A090061.
Showing 1-4 of 4 results.

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

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