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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.)
2
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.
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
KEYWORD
nonn,tabf
AUTHOR
Brian Chess, Sep 17 2022
STATUS
approved