The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A244051 Triangle read by rows in which row n lists the parts of the partitions of n into equal parts, in nonincreasing order. 10
 1, 2, 1, 1, 3, 1, 1, 1, 4, 2, 2, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 6, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 8, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 9, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 5, 5, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row n has length sigma(n) = A000203(n). Row sums give n*A000005(n) = A038040(n). Column 1 is A000027. Both columns 2 and 3 are A032742, n > 1. For any k > 0 and t > 0, the sequence contains exactly one run of k consecutive t's. - Rémy Sigrist, Feb 11 2019 From Omar E. Pol, Dec 04 2019: (Start) The number of parts congruent to 0 mod m in row m*n equals sigma(n) = A000203(n). The number of parts greater than 1 in row n equals A001065(n), the sum of aliquot parts of n. The number of parts greater than 1 and lesser than n in row n equals A048050(n), the sum of divisors of n except 1 and n. The number of partitions in row n equals A000005(n), the number of divisors of n. The number of partitions in row n with an odd number of parts equals A001227(n). 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). The decreasing records in row n give the n-th row of A056538. Row n has n 1's which are all at the end of the row. First n rows contain A000217(n) 1's. The number of k's in row n is A126988(n,k). The number of odd parts in row n is A002131(n). The k-th block in row n has A027750(n,k) parts. Right border gives A000012. (End) LINKS EXAMPLE Triangle begins:    [1];    [2], [1,1];    [3], [1,1,1];    [4], [2,2], [1,1,1,1];    [5], [1,1,1,1,1];    [6], [3,3], [2,2,2], [1,1,1,1,1,1];    [7], [1,1,1,1,1,1,1];    [8], [4,4], [2,2,2,2], [1,1,1,1,1,1,1,1];    [9], [3,3,3], [1,1,1,1,1,1,1,1,1];   [10], [5,5], [2,2,2,2,2], [1,1,1,1,1,1,1,1,1,1];   [11], [1,1,1,1,1,1,1,1,1,1,1];   [12], [6,6], [4,4,4], [3,3,3,3], [2,2,2,2,2,2], [1,1,1,1,1,1,1,1,1,1,1,1];   [13], [1,1,1,1,1,1,1,1,1,1,1,1,1];   [14], [7,7], [2,2,2,2,2,2,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1];   [15], [5,5,5], [3,3,3,3,3], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1];   [16], [8,8], [4,4,4,4], [2,2,2,2,2,2,2,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1];   ... For n = 6 the 11 partitions of 6 are [6], [3, 3], [4, 2], [2, 2, 2], [5, 1], [3, 2], [4, 1, 1], [2, 2, 1, 1], [3, 1, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]. There are only four partitions of 6 that contain equal parts so the 6th row of triangle is [6], [3, 3], [2, 2, 2], [1, 1, 1, 1, 1, 1]. The number of parts equals sigma(6) = A000203(6) = 12. The row sum is A038040(6) = 6*A000005(6) = 6*4 = 24. From Omar E. Pol, Dec 04 2019: (Start) The structure of the above triangle is as follows:    1;    2 11;    3    111;    4 22     1111;    5             11111;    6 33 222            111111;    7                          1111111;    8 44     2222                      11111111;    9    333                                    111111111;   ... (End) PROG (PARI) tabf(nn) = {for (n=1, nn, d = Vecrev(divisors(n)); for (i=1, #d, for (j=1, n/d[i], print1(d[i], ", ")); ); print(); ); } \\ Michel Marcus, Nov 08 2014 CROSSREFS Cf. A000005, A000012, A000041, A000203, A000217, A001065, A001227, A002131, A027750, A032742, A038040, A048050, A056538, A126988, A237593, A245579, A299765, A328365, A309400 (mirror). Sequence in context: A167269 A105535 A182980 * A207974 A239454 A108888 Adjacent sequences:  A244048 A244049 A244050 * A244052 A244053 A244054 KEYWORD nonn,tabf,easy AUTHOR Omar E. Pol, Nov 08 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 29 17:08 EST 2020. Contains 338769 sequences. (Running on oeis4.)