cp's OEIS Frontend

A309400 Irregular triangle read by rows in which row n lists in reverse order the partitions of n into equal parts.

%I A309400 #101 Jan 21 2022 05:06:36
%S A309400 1,1,1,2,1,1,1,3,1,1,1,1,2,2,4,1,1,1,1,1,5,1,1,1,1,1,1,2,2,2,3,3,6,1,
%T A309400 1,1,1,1,1,1,7,1,1,1,1,1,1,1,1,2,2,2,2,4,4,8,1,1,1,1,1,1,1,1,1,3,3,3,
%U A309400 9,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,5,5,10,1,1,1,1,1,1,1,1,1,1,1,11
%N A309400 Irregular triangle read by rows in which row n lists in reverse order the partitions of n into equal parts.
%C A309400 The number of parts in row n equals sigma(n) = A000203(n), the sum of the divisors of n. More generally, the number of parts congruent to 0 (mod m) in row m*n equals sigma(n).
%C A309400 The number of parts greater than 1 in row n equals A001065(n), the sum of the aliquot parts of n.
%C A309400 The number of parts greater than 1 and less than n in row n equals A048050(n), the sum of divisors of n except for 1 and n.
%C A309400 The number of partitions in row n equals A000005(n), the number of divisors of n.
%C A309400 The number of partitions in row n with an odd number of parts equals A001227(n).
%C A309400 The sum of odd parts in row n equals the sum of parts of the partitions in row n that have an odd number of parts, and equals the sum of all parts in the partitions of n into consecutive parts, and equals A245579(n) = n*A001227(n).
%C A309400 The sum of row n equals n*A000005(n) = A038040(n).
%C A309400 Records in row n give the n-th row of A027750.
%C A309400 First n rows contain A000217(n) 1's.
%C A309400 The number of k's in row n is A126988(n,k).
%C A309400 The number of odd parts in row n is A002131(n).
%C A309400 The k-th block in row n has A056538(n,k) parts.
%C A309400 Column 1 gives A000012.
%C A309400 Right border gives A000027.
%e A309400 Triangle begins:
%e A309400 [1];
%e A309400 [1,1], [2];
%e A309400 [1,1,1], [3];
%e A309400 [1,1,1,1], [2,2], [4];
%e A309400 [1,1,1,1,1], [5];
%e A309400 [1,1,1,1,1,1], [2,2,2], [3,3], [6];
%e A309400 [1,1,1,1,1,1,1], [7];
%e A309400 [1,1,1,1,1,1,1,1], [2,2,2,2], [4,4], [8];
%e A309400 [1,1,1,1,1,1,1,1,1], [3,3,3], [9];
%e A309400 [1,1,1,1,1,1,1,1,1,1], [2,2,2,2,2], [5,5], [10];
%e A309400 [1,1,1,1,1,1,1,1,1,1,1], [11];
%e A309400 [1,1,1,1,1,1,1,1,1,1,1,1], [2,2,2,2,2,2], [3,3,3,3], [4,4,4], [6,6], [12];
%e A309400 [1,1,1,1,1,1,1,1,1,1,1,1,1], [13];
%e A309400 [1,1,1,1,1,1,1,1,1,1,1,1,1,1], [2,2,2,2,2,2,2], [7,7], [14];
%e A309400 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], [3,3,3,3,3], [5,5,5], [15];
%e A309400 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], [2,2,2,2,2,2,2,2], [4,4,4,4], [8,8], [16];
%e A309400 ...
%Y A309400 Mirror of A244051.
%Y A309400 Cf. A000005, A000012, A000027, A000203, A000217, A001065, A001227, A002131, A027750, A038040, A048050, A056538, A126988, A237593, A245579, A299765, A328365.
%K A309400 nonn,tabf
%O A309400 1,4
%A A309400 _Omar E. Pol_, Nov 30 2019