|
%I #25 Aug 17 2018 09:26:15
%S 1,2,3,4,5,9,8,6,18,15,16,7,25,21,81,32,10,36,27,162,45,64,11,49,30,
%T 324,63,729,128,12,50,33,625,75,1458,105,256,13,72,35,648,90,2916,135,
%U 225,512,14,98,39,1250,99,5832,165,441,405,1024,17,100,42,1296,117,11664,189,450,567,59049,2048,19,121,51,2401,126,15625
%N Square array read by antidiagonals upwards: T(n,k) = n-th number with k odd divisors.
%C T(n,k) is the n-th positive integer with exactly k odd divisors.
%C This is a permutation of the natural numbers.
%C T(n,k) is also the n-th number j with the property that the symmetric representation of sigma(j) has k subparts (cf. A279387). - _Omar E. Pol_, Dec 27 2016
%C T(n,k) is also the n-th positive integer with exactly k partitions into consecutive parts. - _Omar E. Pol_, Aug 16 2018
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e The corner of the square array begins:
%e 1, 3, 9, 15, 81, 45, 729, 105, 225, 405, ...
%e 2, 5, 18, 21, 162, 63, 1458, 135, 441, 567, ...
%e 4, 6, 25, 27, 324, 75, 2916, 165, 450, 810, ...
%e 8, 7, 36, 30, 625, 90, 5832, 189, 882, 891, ...
%e 16, 10, 49, 33, 648, 99, 11664, 195, 900, 1053, ...
%e 32, 11, 50, 35, 1250, 117, 15625, 210, 1089, 1134, ...
%e 64, 12, 72, 39, 1296, 126, 23328, 231, 1225, 1377, ...
%e 128, 13, 98, 42, 2401, 147, 31250, 255, 1521, 1539, ...
%e ...
%Y Row 1 is A038547.
%Y Column 1-10: A000079, A038550, A072502, apparently A131651, A267696, A230577, A267697, A267891, A267892, A267893.
%Y Cf. A001227, A182469, A236104, A237591, A237593, A240062, A261697, A261698, A261699, A279387, A286000, A286001, A296508.
%K nonn,tabl
%O 1,2
%A _Omar E. Pol_, Apr 02 2016
|
