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 A209082 Least power separator of the partitions of n. 1
 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The least power separator of the partitions of n is introduced here as the least positive integer m for which the sums x(1)^m + x(2)^m + ... + x(k)^m, as {x(1),x(2),...,x(k)} ranges through the partitions of n (as in A000041), are distinct. In the following table, d(n,h)=[number of partitions x(1),x(2),...,x(k) of n]-[number of distinct sums x(1)^m + x(2)^m + ... + x(k)^m], so that a(n) is the least h for which d(n,h)=0. n.....d(n,1)..d(n,2)..d(n,3)..d(n,4)..d(n,5)..d(n,6) 1.....0.......0.......0.......0.......0.......0 2.....1.......0.......0.......0.......0.......0 3.....2.......0.......0.......0.......0.......0 4.....4.......0.......0.......0.......0.......0 5.....6.......0.......0.......0.......0.......0 6.....10......2.......0.......0.......0.......0 7.....14......2.......0.......0.......0.......0 8.....21......4.......2.......0.......0.......0 9.....29......9.......3.......0.......0.......0 10....41......15......6.......0.......0.......0 11....55......24......1.......0.......0.......0 12....76......38......16......0.......0.......0 13....100.....55......24......1.......0.......0 14....134.....81......39......1.......0.......0 15....175.....115.....61......2.......0.......0 16....230.....159.....91......3.......4.......0 17....296.....214.....130.....5.......7.......0 18....384.....293.....186.....7.......12......0 19....489.....384.....254.....12......20......0 20....626.....509.....349.....16......33......0...1...0 21....791.....662.....467.....27......48......0...1...0 22....1001....857.....625.....40......79......0...2...0 For 0m but not for 19

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Last modified December 13 18:07 EST 2018. Contains 318086 sequences. (Running on oeis4.)