A355079 Irregular triangle read by rows: the first row is 1, and the n-th row (n > 1) lists the factors f of n where n/f is prime (the maximal factors of n.)

1, 1, 1, 2, 1, 2, 3, 1, 4, 3, 2, 5, 1, 4, 6, 1, 2, 7, 3, 5, 8, 1, 6, 9, 1, 4, 10, 3, 7, 2, 11, 1, 8, 12, 5, 2, 13, 9, 4, 14, 1, 6, 10, 15, 1, 16, 3, 11, 2, 17, 5, 7, 12, 18, 1, 2, 19, 3, 13, 8, 20, 1, 6, 14, 21, 1, 4, 22, 9, 15, 2, 23, 1, 16, 24, 7, 10, 25

Offset

1,4

Comments

If n is prime, then 1 is its only maximal factor.

In order for a player to select a number in the game Taxman, at least one of the number's maximal factors must be available to be claimed by the taxman.

Links

Table of n, a(n) for n=1..78.

Formula

T(n,k) = n / A302170(n,k).

Example

Triangle begins:
   1:  1
   2:  1
   3:  1
   4:  2
   5:  1
   6:  2 3
   7:  1
   8:  4
   9:  3
  10:  2 5
  11:  1
  12:  4 6
  13:  1
  14:  2 7
  15:  3 5
  16:  8
  17:  1
  18:  6 9
  19:  1
  20:  4 10

Mathematica

Table[n / Reverse @ FactorInteger[n][[;; , 1]], {n, 1, 50}] // Flatten (* Amiram Eldar, Sep 21 2022 *)

Prog

(Haskell)
a355079 n k = a355079_tabl !! (n-1) !! (k-1)
a355079_tabl = map a355079_row [1..]
a355079_row n = [div n x | x <- a302170_row n]
(Python)
from sympy import factorint
def row(n): return [1] if n < 2 else sorted(n//p for p in factorint(n))
print([an for r in range(1, 51) for an in row(r)]) # Michael S. Branicky, Sep 18 2022
(PARI) row(n) = if (n==1, [1], select(x->isprime(n/x), divisors(n))); \\ Michel Marcus, Sep 21 2022

Crossrefs

Cf. A019312 (taxman sequence), A302170.

Sequence in context: A133299 A286537 A132163 * A205682 A217762 A172467

Adjacent sequences: A355076 A355077 A355078 * A355080 A355081 A355082

Keyword

nonn,tabf

Author

Brian Chess, Sep 17 2022

Status

approved