cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A341339 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.

This page as a plain text file.
%I A341339 #70 Aug 05 2021 10:38:43
%S A341339 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 A341339 251,121,62,16,12,0,0,0,509,169,125,16,32,0,0,0,0,1021,361,254,81,63,
%U A341339 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 A341339 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 A341339 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 A341339 Diagonal of the square array contains sequential powers of 2 since 2^k has exactly k+1 divisors.
%H A341339 Serguei Zolotov, <a href="/A341339/b341339.txt">Antidiagonals of table of n, a(n) for n = 2..2081</a>
%H A341339 Serguei Zolotov, <a href="/A341339/a341339_1.txt">Python script to generate A341339 combining different methods</a>
%e A341339 Array begins:
%e A341339      k = 1   2   3    4    5    6    7    8    9    10    11    12
%e A341339 -------------------------------------------------------------
%e A341339 n = 2  | 2,  3,  7,  13,  31,  61, 127, 251, 509, 1021, 2039, 4093, ...
%e A341339 n = 3  | 0,  4,  4,   9,  25,  49, 121, 169, 361,  961, 1849, 3721, ...
%e A341339 n = 4  | 0,  0,  8,  15,  27,  62, 125, 254, 511, 1018, 2047, 4087, ...
%e A341339 n = 5  | 0,  0,  0,  16,  16,  16,  81,  81,  81,  625,  625, 2401, ...
%e A341339 n = 6  | 0,  0,  0,  12,  32,  63, 124, 245, 508, 1017, 2043, 4084, ...
%e A341339 n = 7  | 0,  0,  0,   0,   0,  64,  64,  64,  64,  729,  729,  729, ...
%e A341339 n = 8  | 0,  0,  0,   0,  30,  56, 128, 255, 506, 1023, 2037, 4094, ...
%e A341339 n = 9  | 0,  0,  0,   0,   0,  36, 100, 256, 484,  676, 1521, 3844, ...
%e A341339 n = 10 | 0,  0,  0,   0,   0,  48, 112, 208, 512,  976, 2032, 4016, ...
%e A341339 n = 11 | 0,  0,  0,   0,   0,   0,   0,   0,   0, 1024, 1024, 1024, ...
%e A341339 n = 12 | 0,  0,  0,   0,   0,  60, 126, 234, 500, 1014, 2048, 4086, ...
%e A341339 n = 13 | 0,  0,  0,   0,   0,   0,   0,   0,   0,    0,    0, 4096, ...
%e A341339 ...
%o A341339 (Python)
%o A341339 import sympy
%o A341339 # k = 1,2,3,...
%o A341339 # n = 2,3,4,...
%o A341339 def a(k, n):
%o A341339     a = 2**k
%o A341339     while a > 0 and sympy.divisor_count(a) != n:
%o A341339         a = a - 1
%o A341339     return a
%K A341339 nonn,tabl
%O A341339 2,1
%A A341339 _Serguei Zolotov_, Apr 27 2021