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%I #70 Aug 05 2021 10:38:43
%S 2,3,0,7,4,0,13,4,0,0,31,9,8,0,0,61,25,15,0,0,0,127,49,27,16,0,0,0,
%T 251,121,62,16,12,0,0,0,509,169,125,16,32,0,0,0,0,1021,361,254,81,63,
%U 0,0,0,0,0,2039,961,511,81,124,64,30,0,0,0,0,4093,1849,1018,81,245,64,56,0,0,0,0,0
%N Square array read by descending antidiagonals where the row n (n >= 2) and column k (k >= 1) contains the largest number not greater than 2^k that has exactly n divisors, or 0 if such a number does not exist.
%C 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.
%C Diagonal of the square array contains sequential powers of 2 since 2^k has exactly k+1 divisors.
%H Serguei Zolotov, <a href="/A341339/b341339.txt">Antidiagonals of table of n, a(n) for n = 2..2081</a>
%H Serguei Zolotov, <a href="/A341339/a341339_1.txt">Python script to generate A341339 combining different methods</a>
%e Array begins:
%e k = 1 2 3 4 5 6 7 8 9 10 11 12
%e -------------------------------------------------------------
%e n = 2 | 2, 3, 7, 13, 31, 61, 127, 251, 509, 1021, 2039, 4093, ...
%e n = 3 | 0, 4, 4, 9, 25, 49, 121, 169, 361, 961, 1849, 3721, ...
%e n = 4 | 0, 0, 8, 15, 27, 62, 125, 254, 511, 1018, 2047, 4087, ...
%e n = 5 | 0, 0, 0, 16, 16, 16, 81, 81, 81, 625, 625, 2401, ...
%e n = 6 | 0, 0, 0, 12, 32, 63, 124, 245, 508, 1017, 2043, 4084, ...
%e n = 7 | 0, 0, 0, 0, 0, 64, 64, 64, 64, 729, 729, 729, ...
%e n = 8 | 0, 0, 0, 0, 30, 56, 128, 255, 506, 1023, 2037, 4094, ...
%e n = 9 | 0, 0, 0, 0, 0, 36, 100, 256, 484, 676, 1521, 3844, ...
%e n = 10 | 0, 0, 0, 0, 0, 48, 112, 208, 512, 976, 2032, 4016, ...
%e n = 11 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 1024, 1024, 1024, ...
%e n = 12 | 0, 0, 0, 0, 0, 60, 126, 234, 500, 1014, 2048, 4086, ...
%e n = 13 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4096, ...
%e ...
%o (Python)
%o import sympy
%o # k = 1,2,3,...
%o # n = 2,3,4,...
%o def a(k, n):
%o a = 2**k
%o while a > 0 and sympy.divisor_count(a) != n:
%o a = a - 1
%o return a
%K nonn,tabl
%O 2,1
%A _Serguei Zolotov_, Apr 27 2021
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