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 A221649 Tetrahedron E(n,j,k) = k*T(j,k)*p(n-k), where T(j,k) = 1 if k divides j otherwise 0. 1
 1, 1, 1, 2, 2, 1, 2, 1, 0, 3, 3, 2, 4, 1, 0, 3, 1, 0, 2, 4, 5, 3, 6, 2, 0, 6, 1, 0, 2, 4, 1, 0, 0, 0, 5, 7, 5, 10, 3, 0, 9, 2, 4, 0, 8, 1, 0, 0, 0, 5, 1, 2, 3, 0, 0, 6, 11, 7, 14, 5, 0, 15, 3, 6, 0, 12, 2, 0, 0, 0, 10, 1, 2, 3, 0, 0, 6, 1, 0, 0, 0, 0, 0, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The tetrahedron shows a connection between divisors and partitions. The sum of all elements of slice n is A066186(n). The sum of row j of slice n is A221529(n,j). The sum of column k of slice n is A138785(n,k), the sum of all parts of size k in all partitions of n. See also the tetrahedron of A221650. LINKS FORMULA E(n,j,k) = k*A051731(j,k)*A000041(n-j) = A127093(j,k)*A000041(n-j) = k*A221650(n,j,k). EXAMPLE First six slices of tetrahedron are --------------------------------------------------- n  j / k   1  2  3  4  5  6      A221529   A066186 --------------------------------------------------- 1  1       1,                       1         1 ................................................... 2  1       1,                       1 2  2       1, 2,                    3         4 ................................................... 3  1       2,                       2 3  2       1, 2,                    3 3  3       1, 0, 3,                 4         9 ................................................... 4  1       3,                       3 4  2       2, 4,                    6 4  3       1, 0, 3,                 4 4  4       1, 2, 0, 4,              7        20 ................................................... 5  1       5,                       5 5  2       3, 6,                    9 5, 3,      2, 0, 6,                 8 5, 4,      1, 2, 0, 4,              7 5, 5,      1, 0, 0, 0, 5,           6        35 ................................................... 6  1       7,                       7 6  2       5, 10,                  15 6  3       3, 0, 9,                12 6  4       2, 4, 0, 8,             14 6  5       1, 0, 0, 0, 5,           6 6  6       1, 2, 3, 0, 0, 6,       12        66 ................................................... CROSSREFS Cf. A000005, A000041, A000203, A027750, A051731, A066186, A127093, A138785, A221529, A221650. Sequence in context: A284478 A298948 A085906 * A090406 A152723 A237497 Adjacent sequences:  A221646 A221647 A221648 * A221650 A221651 A221652 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Jan 21 2013 STATUS approved

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Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)