A343902 Irregular array read by rows: T(n, k) is the k-th prime p such that (p-1)|A000010(n).

2, 2, 2, 3, 2, 3, 2, 3, 5, 2, 3, 2, 3, 7, 2, 3, 5, 2, 3, 7, 2, 3, 5, 2, 3, 11, 2, 3, 5, 2, 3, 5, 7, 13, 2, 3, 7, 2, 3, 5, 2, 3, 5, 2, 3, 5, 17, 2, 3, 7, 2, 3, 7, 19, 2, 3, 5, 2, 3, 5, 7, 13, 2, 3, 11, 2, 3, 23, 2, 3, 5, 2, 3, 5, 11, 2, 3, 5, 7, 13, 2, 3, 7, 19

Offset

1,1

Links

Table of n, a(n) for n=1..84.

Example

The irregular array T starts as follows:
   n | T(n, k)
  ---+---------------
   1 | 2
   2 | 2
   3 | 2, 3
   4 | 2, 3
   5 | 2, 3, 5
   6 | 2, 3
   7 | 2, 3, 7
   8 | 2, 3, 5
   9 | 2, 3, 7
  10 | 2, 3, 5
  11 | 2, 3, 11
  12 | 2, 3, 5
  13 | 2, 3, 5, 7, 13
  14 | 2, 3, 7
  15 | 2, 3, 5
  16 | 2, 3, 5
  17 | 2, 3, 5, 17
  18 | 2, 3, 7
  19 | 2, 3, 7, 19
  20 | 2, 3, 5
  21 | 2, 3, 5, 7, 13
  22 | 2, 3, 11
  23 | 2, 3, 23
  24 | 2, 3, 5
  25 | 2, 3, 5, 11
  26 | 2, 3, 5, 7, 13
  27 | 2, 3, 7, 19
  28 | 2, 3, 5, 7, 13
  29 | 2, 3, 5, 29
  30 | 2, 3, 5

Mathematica

row[n_] := Select[Divisors[EulerPhi[n]], PrimeQ[# + 1] &] + 1; Array[row, 30] // Flatten (* Amiram Eldar, Dec 06 2024 *)

Prog

(PARI) row(n) = my(e=eulerphi(n)); forprime(p=2, e+1, if(e%(p-1)==0, print1(p, ", "))); print("") \\ corrected by Amiram Eldar, Dec 06 2024
array(rows) = for(x=3, rows+2, row(x))
array(10) \\ Print upper 10 rows of the array
(PARI) row(n) = apply(x -> x+1, select(x -> isprime(x+1), divisors(eulerphi(n)))); \\ Amiram Eldar, Dec 06 2024

Crossrefs

Cf. A000010, A343901 (row lengths), A343903.

Sequence in context: A145193 A292585 A175872 * A143117 A108053 A076221

Adjacent sequences: A343899 A343900 A343901 * A343903 A343904 A343905

Keyword

nonn,tabf

Author

Felix Fröhlich, May 03 2021

Extensions

Offset changed to 1 and data corrected by Amiram Eldar, Dec 06 2024

Status

approved