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 A212120 Triangle read by rows T(n,k), n>=1, k>=1, where T(n,k) is the sum of the divisors d of n with min(d, n/d) = k. 6
 1, 3, 5, 7, 1, 9, 1, 11, 3, 13, 3, 15, 5, 17, 5, 1, 19, 7, 1, 21, 7, 1, 23, 9, 3, 25, 9, 3, 27, 11, 3, 29, 11, 5, 31, 13, 5, 1, 33, 13, 5, 1, 35, 15, 7, 1, 37, 15, 7, 1, 39, 17, 7, 3, 41, 17, 9, 3, 43, 19, 9, 3, 45, 19, 9, 3, 47, 21, 11, 5, 49, 21, 11, 5, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Column k lists the odd numbers repeated k times starting in row k^2. 1 together with the first differences of the row sums give the divisor function A000005. T(n,k) is also the total number of divisors of all positive integers <= n on the edges of k-th triangle in the diagram of divisors (see link section). See also A212119. LINKS Omar E. Pol, , Diagram of divisors, figure 1, figure 2 FORMULA T(n,k) = Sum_{j=1..n) A212119(j,k). EXAMPLE Written as an irregular triangle the sequence begins: 1; 3; 5; 7,   1; 9,   1; 11,  3; 13,  3; 15,  5; 17,  5,  1; 19,  7,  1; 21,  7,  1; 23,  9,  3; 25,  9,  3; 27, 11,  3; 29, 11,  5; 31, 13,  5,  1; 33, 13,  5,  1; 35, 15,  7,  1; 37, 15,  7,  1; 39, 17,  7,  3; 41, 17,  9,  3; 43, 19,  9,  3; 45, 19,  9,  3; 47, 21, 11,  5; 49, 21, 11,  5,  1; CROSSREFS Row sums give A006218, n >= 1. Columns (1-5): A005408, A109613, A130823, A129756, A130497. Cf. A000005, A027750, A010766, A147861, A163100, A212119. Sequence in context: A266295 A172049 A021032 * A128059 A084763 A179650 Adjacent sequences:  A212117 A212118 A212119 * A212121 A212122 A212123 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Jul 02 2012 EXTENSIONS Definition changed by Franklin T. Adams-Watters, Jul 12 2012 STATUS approved

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Last modified June 19 04:44 EDT 2019. Contains 324217 sequences. (Running on oeis4.)