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 A278118 Irregular triangle T(n,k) = A278113(n,k) for 1 <= k <= A278116(n), read by rows. 4
 1, 2, 1, 3, 2, 1, 4, 3, 2, 5, 4, 3, 2, 6, 4, 3, 7, 5, 8, 6, 9, 7, 5, 4, 3, 10, 8, 6, 5, 11, 8, 6, 5, 12, 9, 13, 10, 14, 11, 8, 15, 12, 9, 16, 13, 10, 8, 6, 17, 13, 10, 18, 14, 19, 15, 20, 16, 12, 10, 21, 17, 13, 22, 17, 13, 23, 18, 24, 19, 25, 20, 15, 26, 21, 16, 13, 27, 22, 17, 14, 11, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This triangle lists the "descending sequences for rank 1" of Eggleton et al. REFERENCES R. B. Eggleton, J. S. Kimberley and J. A. MacDougall, Square-free rank of integers, submitted. LINKS Jason Kimberley, Table of i, a(i) for i = 1..10104 (T(n,k) for n = 1..3333) FORMULA From A278113: T(n,k) sqrt(prime(k)) <= n sqrt(2) < (T(n,k)+1) sqrt(prime(k)). Here, we also have: T(n,1) sqrt(2) > T(n,2) sqrt(3) > ... > T(n,A278116(n)) sqrt(prime(A278116(n))). EXAMPLE For example, 6 sqrt(2) > 4 sqrt(3) > 3 sqrt(5), because 72 > 48 > 45. The first six rows are: 1; 2, 1; 3, 2, 1; 4, 3, 2; 5, 4, 3, 2; 6, 4, 3; MATHEMATICA Function[w, MapIndexed[Take[w[[First@ #2, 1]], 1 + Length@ TakeWhile[ Differences@ #1, # < 0 &]] &, w[[All, -1]]]]@ Table[Function[k, Function[p, {#, p #^2} &@ Floor[n Sqrt[2/p]]]@ Prime@ k]@ Range@ PrimePi[2 n^2], {n, 27}] (* Michael De Vlieger, Feb 17 2017 *) PROG (Magma) A278112:=func; A278115_row:=func; A278116:=func; A278118_row:=func; [A278118_row(n):n in[1..20]]; CROSSREFS Cf. A278104. Sequence in context: A227539 A133334 A003603 * A255238 A212536 A188277 Adjacent sequences: A278115 A278116 A278117 * A278119 A278120 A278121 KEYWORD nonn,tabf,easy AUTHOR Jason Kimberley, Feb 12 2017 STATUS approved

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Last modified November 27 03:04 EST 2022. Contains 358362 sequences. (Running on oeis4.)