cp's OEIS Frontend

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.)

%I A355079 #39 Sep 22 2022 18:20:31
%S A355079 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 A355079 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 A355079 1,6,14,21,1,4,22,9,15,2,23,1,16,24,7,10,25
%N 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.)
%C A355079 If n is prime, then 1 is its only maximal factor.
%C A355079 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 A355079 T(n,k) = n / A302170(n,k).
%e A355079 Triangle begins:
%e A355079    1:  1
%e A355079    2:  1
%e A355079    3:  1
%e A355079    4:  2
%e A355079    5:  1
%e A355079    6:  2 3
%e A355079    7:  1
%e A355079    8:  4
%e A355079    9:  3
%e A355079   10:  2 5
%e A355079   11:  1
%e A355079   12:  4 6
%e A355079   13:  1
%e A355079   14:  2 7
%e A355079   15:  3 5
%e A355079   16:  8
%e A355079   17:  1
%e A355079   18:  6 9
%e A355079   19:  1
%e A355079   20:  4 10
%t A355079 Table[n / Reverse @ FactorInteger[n][[;;, 1]], {n, 1, 50}] // Flatten (* _Amiram Eldar_, Sep 21 2022 *)
%o A355079 (Haskell)
%o A355079 a355079 n k = a355079_tabl !! (n-1) !! (k-1)
%o A355079 a355079_tabl = map a355079_row [1..]
%o A355079 a355079_row n = [div n x | x <- a302170_row n]
%o A355079 (Python)
%o A355079 from sympy import factorint
%o A355079 def row(n): return [1] if n < 2 else sorted(n//p for p in factorint(n))
%o A355079 print([an for r in range(1, 51) for an in row(r)]) # _Michael S. Branicky_, Sep 18 2022
%o A355079 (PARI) row(n) = if (n==1, [1], select(x->isprime(n/x), divisors(n))); \\ _Michel Marcus_, Sep 21 2022
%Y A355079 Cf. A019312 (taxman sequence), A302170.
%K A355079 nonn,tabf
%O A355079 1,4
%A A355079 _Brian Chess_, Sep 17 2022