OFFSET
2,1
COMMENTS
First row contains largest prime not greater than 2^k (where k is a column number starting with 1). Second row contains largest square of prime not greater than 2^k.
Diagonal of the square array contains sequential powers of 2 since 2^k has exactly k+1 divisors.
LINKS
Serguei Zolotov, Antidiagonals of table of n, a(n) for n = 2..2081
Serguei Zolotov, Python script to generate A341339 combining different methods
EXAMPLE
Array begins:
k = 1 2 3 4 5 6 7 8 9 10 11 12
-------------------------------------------------------------
n = 2 | 2, 3, 7, 13, 31, 61, 127, 251, 509, 1021, 2039, 4093, ...
n = 3 | 0, 4, 4, 9, 25, 49, 121, 169, 361, 961, 1849, 3721, ...
n = 4 | 0, 0, 8, 15, 27, 62, 125, 254, 511, 1018, 2047, 4087, ...
n = 5 | 0, 0, 0, 16, 16, 16, 81, 81, 81, 625, 625, 2401, ...
n = 6 | 0, 0, 0, 12, 32, 63, 124, 245, 508, 1017, 2043, 4084, ...
n = 7 | 0, 0, 0, 0, 0, 64, 64, 64, 64, 729, 729, 729, ...
n = 8 | 0, 0, 0, 0, 30, 56, 128, 255, 506, 1023, 2037, 4094, ...
n = 9 | 0, 0, 0, 0, 0, 36, 100, 256, 484, 676, 1521, 3844, ...
n = 10 | 0, 0, 0, 0, 0, 48, 112, 208, 512, 976, 2032, 4016, ...
n = 11 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 1024, 1024, 1024, ...
n = 12 | 0, 0, 0, 0, 0, 60, 126, 234, 500, 1014, 2048, 4086, ...
n = 13 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4096, ...
...
PROG
(Python)
import sympy
# k = 1, 2, 3, ...
# n = 2, 3, 4, ...
def a(k, n):
a = 2**k
while a > 0 and sympy.divisor_count(a) != n:
a = a - 1
return a
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Serguei Zolotov, Apr 27 2021
STATUS
approved