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.

A289172 Irregular triangle read by rows: row n lists terms m of A038566(n) such that A001221(m) = A051265(n), with a(1) = 1.

Original entry on oeis.org

1, 1, 2, 3, 2, 3, 4, 5, 6, 3, 5, 7, 2, 4, 5, 7, 8, 3, 7, 9, 6, 10, 5, 7, 11, 6, 10, 12, 3, 5, 9, 11, 13, 14, 15, 6, 10, 12, 14, 15, 5, 7, 11, 13, 17, 6, 10, 12, 14, 15, 18, 3, 7, 9, 11, 13, 17, 19, 10, 20, 15, 21, 6, 10, 12, 14, 15, 18, 20, 21, 22, 5, 7, 11
Offset: 1

Views

Author

Michael De Vlieger, Aug 11 2017

Keywords

Comments

Consider A051265(n), the largest value of A001221(m) for 1 <= m <= n such that gcd(m, n) = 1 (i.e., m is in the reduced residue system or RRS of n, or m is a totative of n). Row n of this sequence consists of m in RRS(n) such that omega(m) = A051265(n).

Examples

			Triangle begins:
   n    T(n,m)                        A051265(n)
   1:   1                                     0
   2:   1                                     0
   3:   2                                     1
   4:   3                                     1
   5:   2    3    4                           1
   6:   5                                     1
   7:   6                                     2
   8:   3    5    7                           1
   9:   2    4    5    7    8                 1
  10:   3    7    9                           1
  11:   6   10                                2
  12:   5    7   11                           1
  13:   6   10   12                           2
  14:   3    5    9   11   13                 1
  15:  14                                     2
  16:  15                                     2
  17:   6   10   12   14   15                 2
  18:   5    7   11   13   17                 1
  19:   6   10   12   14   15   18            2
  20:   3    7    9   11   13   17   19       1

Links

Crossrefs

Cf. A001221, A002110, A038566, A048597, A051250, A051265, A051266, A051267, A051268.

Programs

  • Mathematica
    Table[MaximalBy[#, Last][[All, 1]] &@ Map[{#, PrimeNu@ #} &, Cases[Range[n - 1], k_ /; CoprimeQ[n, k]]] /. {} -> {1}, {n, 30}] // Flatten (* Michael De Vlieger, Aug 11 2017 *)

A051266 Numbers n such that maximal value of prime divisors of reduced residue system for n is 2.

Original entry on oeis.org

7, 11, 13, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 32, 33, 34, 35, 36, 38, 39, 40, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 62, 63, 64, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

Largest value of A001221(k) = 2 for 1 <= k <= n such that gcd (k, n) = 1, i.e., k in row n of A038566. - Michael De Vlieger, Aug 10 2017

Examples

			n = 29 is here because for terms of RRS(29) = {1, 2, ..., 27, 28} the number of prime divisors is 0(for 1), 1(for prime powers) or 2 (for 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28).

Links

Crossrefs

Cf. A001221, A002110, A038566, A048597, A051250, A051265, A051267, A051268.

Programs

  • Mathematica
    Block[{n = 2, P}, P = Product[Prime@ i, {i, n}]; P + Position[#, n][[All, 1]] &@ Array[Max@ Map[PrimeNu, Cases[Range@ #, k_ /; CoprimeQ[#, k]]] &, 120, P + 1]] (* Michael De Vlieger, Aug 10 2017 *)

A051267 Numbers n such that maximal value of prime divisors of reduced residue system for n is 3.

Original entry on oeis.org

31, 37, 41, 43, 47, 49, 53, 55, 59, 61, 65, 67, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 106, 107, 109, 111, 113, 115, 116, 117, 118, 119, 121, 122, 123, 124, 125, 127, 128, 129, 131, 133, 134, 136, 137, 139, 141, 142, 143, 145, 146, 147
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

Largest value of A001221(k) = 3 for 1 <= k <= n such that gcd(k, n) = 1, i.e., k in row n of A038566. - Michael De Vlieger, Aug 10 2017

Links

Crossrefs

Cf. A001221, A002110, A038566, A048597, A051250, A051265, A051266, A051268.

Programs

  • Mathematica
    Block[{n = 3, P}, P = Product[Prime@ i, {i, n}]; P + Position[#, n][[All, 1]] &@ Array[Max@ Map[PrimeNu, Cases[Range@ #, k_ /; CoprimeQ[#, k]]] &, 117, P + 1]] (* Michael De Vlieger, Aug 10 2017 *)

A051268 Numbers n such that maximal value of prime divisors of reduced residue system for n is 4.

Original entry on oeis.org

211, 221, 223, 227, 229, 233, 239, 241, 247, 251, 253, 257, 263, 269, 271, 277, 281, 283, 289, 293, 299, 307, 311, 313, 317, 319, 323, 331, 337, 341, 343, 347, 349, 353, 359, 361, 367, 371, 373, 377, 379, 383, 389, 391, 397, 401, 403, 407, 409, 413
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

Largest value of A001221(k) = 4 for 1 <= k <= n such that gcd(k, n) = 1, i.e., k in row n of A038566. - Michael De Vlieger, Aug 10 2017

Links

Crossrefs

Cf. A001221, A002110, A006862, A038566, A048597, A051250, A051265, A051266, A051267.

Programs

  • Mathematica
    Block[{n = 4, P}, P = Product[Prime@ i, {i, n}]; P + Position[#, n][[All, 1]] &@ Array[Max@ Map[PrimeNu, Cases[Range@ #, k_ /; CoprimeQ[#, k]]] &, 175, P + 1]] (* Michael De Vlieger, Aug 10 2017 *)

Extensions

More terms from Michael De Vlieger, Aug 10 2017
Showing 1-4 of 4 results.

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