A355079 - OEIS

%I #39 Sep 22 2022 18:20:31

%S 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,

%T 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,

%U 1,6,14,21,1,4,22,9,15,2,23,1,16,24,7,10,25

%N 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.)

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

%C 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.

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

%e Triangle begins:

%e    1:  1

%e    2:  1

%e    3:  1

%e    4:  2

%e    5:  1

%e    6:  2 3

%e    7:  1

%e    8:  4

%e    9:  3

%e   10:  2 5

%e   11:  1

%e   12:  4 6

%e   13:  1

%e   14:  2 7

%e   15:  3 5

%e   16:  8

%e   17:  1

%e   18:  6 9

%e   19:  1

%e   20:  4 10

%t Table[n / Reverse @ FactorInteger[n][[;;, 1]], {n, 1, 50}] // Flatten (* _Amiram Eldar_, Sep 21 2022 *)

%o (Haskell)

%o a355079 n k = a355079_tabl !! (n-1) !! (k-1)

%o a355079_tabl = map a355079_row [1..]

%o a355079_row n = [div n x | x <- a302170_row n]

%o (Python)

%o from sympy import factorint

%o def row(n): return [1] if n < 2 else sorted(n//p for p in factorint(n))

%o print([an for r in range(1, 51) for an in row(r)]) # _Michael S. Branicky_, Sep 18 2022

%o (PARI) row(n) = if (n==1, [1], select(x->isprime(n/x), divisors(n))); \\ _Michel Marcus_, Sep 21 2022

%Y Cf. A019312 (taxman sequence), A302170.

%K nonn,tabf

%O 1,4

%A _Brian Chess_, Sep 17 2022