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
Examples
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
Programs
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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]
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Mathematica
Table[n / Reverse @ FactorInteger[n][[;;, 1]], {n, 1, 50}] // Flatten (* Amiram Eldar, Sep 21 2022 *) -
PARI
row(n) = if (n==1, [1], select(x->isprime(n/x), divisors(n))); \\ Michel Marcus, Sep 21 2022
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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
Formula
T(n,k) = n / A302170(n,k).
Comments