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.

A345250 a(n) is the number of divisors of A344422(n).

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 18, 28, 36, 42, 48, 72, 96, 108, 128, 144, 168, 192, 336, 384, 448, 504, 672, 896, 960, 1008, 1134, 1296, 1344, 2560, 2592, 3456, 3584, 4320, 4608, 5376, 6144, 6336, 6912, 9216, 10240, 12288, 13824, 15360, 16128, 16384, 20736, 23328, 24576
Offset: 1

Views

Author

Bhupendra Kumar Singh, Jun 12 2021

Keywords

Comments

Sequence proposed by Felix Fröhlich in the first comment of A344422.

Crossrefs

Records in A076888.

Formula

a(n) = A000005(A344422(n)).

A345260 a(n) = A000203(A344422(n)).

Original entry on oeis.org

1, 3, 7, 12, 84, 144, 728, 6096, 8736, 19812, 85120, 163520, 738720, 871416, 2419200, 2935296, 7567168, 15193920, 84319872, 169303680, 259445760, 934545248, 8600626944, 9438363648, 19853729280, 34805721600, 87037870374, 165451302016, 254879514624, 957538713600
Offset: 1

Views

Author

Bhupendra Kumar Singh, Jun 12 2021

Keywords

Crossrefs

A343735 Odd palindromes having more divisors than all smaller odd palindromes.

Original entry on oeis.org

1, 3, 9, 33, 99, 525, 3003, 5445, 5775, 50505, 53235, 171171, 525525, 5073705, 18999981, 50555505, 51666615, 512272215, 513828315, 5026226205, 5053553505, 5184994815, 5708778075, 52252425225, 502299992205, 502875578205, 524241142425, 579024420975
Offset: 1

Views

Author

Jon E. Schoenfield, Jun 22 2021

Keywords

Comments

A000005(a(n)) = A343736(n).
Conjectures:
(1) All terms after a(1)=1 are multiples of 3.
(2) The number of terms after a(30)=34418522581443 that are not multiples of 5 is finite but not zero.

Examples

			                                                      no. of
   n        a(n)  prime factorization                divisors
  --  ----------  ---------------------------------  --------
   1           1  -                                         1
   2           3  3                                         2
   3           9  3^2                                       3
   4          33  3 * 11                                    4
   5          99  3^2 * 11                                  6
   6         525  3 * 5^2 * 7                              12
   7        3003  3 * 7 * 11 * 13                          16
   8        5445  3^2 * 5 * 11^2                           18
   9        5775  3 * 5^2 * 7 * 11                         24
  10       50505  3 * 5 * 7 * 13 * 37                      32
  11       53235  3^2 * 5 * 7 * 13^2                       36
  12      171171  3^2 * 7 * 11 * 13 * 19                   48
  13      525525  3 * 5^2 * 7^2 * 11 * 13                  72
  14     5073705  3^3 * 5 * 7^2 * 13 * 59                  96
  15    18999981  3^3 * 7 * 11 * 13 * 19 * 37             128
  16    50555505  3 * 5 * 7^2 * 11 * 13^2 * 37            144
  17    51666615  3^2 * 5 * 7 * 11 * 13 * 31 * 37         192
  18   512272215  3^3 * 5 * 7^3 * 13 * 23 * 37            256
  19   513828315  3^2 * 5 * 7 * 11^2 * 13 * 17 * 61       288
  20  5026226205  3 * 5 * 7^2 * 11 * 13 * 17 * 29 * 97    384
		

Crossrefs

Cf. A000005, A002113 (palindromes), A076888 (their number of divisors), A029950 (odd palindromes), A344422, A345250, A343736.

A343736 a(n) is the number of divisors of A343735(n).

Original entry on oeis.org

1, 2, 3, 4, 6, 12, 16, 18, 24, 32, 36, 48, 72, 96, 128, 144, 192, 256, 288, 384, 432, 512, 576, 648, 768, 1024, 1296, 1536, 1728, 2048, 2304, 2592, 3456, 3888, 4608, 5760, 6912, 7680, 8640, 9216, 12288, 13824, 15360, 17280, 18432, 20480, 23040, 30720, 34560
Offset: 1

Views

Author

Jon E. Schoenfield, Jun 22 2021

Keywords

Crossrefs

Cf. A000005, A002113 (palindromes), A076888 (their number of divisors), A029950 (odd palindromes), A343735, A344422, A345250.

Formula

a(n) = A000005(A343735(n)).
Showing 1-4 of 4 results.