A382926 Irregular table where row n lists numbers k in row n of A162306 for which there exists a prime p | n such that k*p > n.
2, 3, 4, 5, 3, 4, 6, 7, 8, 9, 4, 5, 8, 10, 11, 6, 8, 9, 12, 13, 4, 7, 8, 14, 5, 9, 15, 16, 17, 8, 9, 12, 16, 18, 19, 5, 8, 10, 16, 20, 7, 9, 21, 4, 8, 11, 16, 22, 23, 9, 12, 16, 18, 24, 25, 4, 8, 13, 16, 26, 27, 7, 8, 14, 16, 28, 29, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30
Offset: 2
Examples
Let s(n) = A382964(n). Table of select rows: n s(n) row n of this sequence -------------------------------------------------------- 6 3 3, 4, 6; 10 4 4, 5, 8, 10; 12 4 6, 8, 9, 12; 14 4 4, 7, 8, 14; 15 3 5, 9, 15; 18 5 8, 9, 12, 16, 18; 20 5 5, 8, 10, 16, 20; 21 3 7, 9, 21; 22 5 4, 8, 11, 16, 22; 24 5 9, 12, 16, 18, 24; 26 5 4, 8, 13, 16, 26; 28 5 7, 8, 14, 16, 28; 30 12 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30. In the examples below, we place terms in row n in brackets [] among other terms in row n of A162306, presented in order of row n of A275280. Row p^m for m > 0 and prime p is {p^m}, since multiplying p^m by p exceeds p^m. Row 10 = {4, 5, 8, 10}, since numbers k such that rad(k) | 10 contains these numbers, furthermore, we have the following: 2 or 5 times 8 exceeds 10, 5*4 > 10, 2 or 5 times 10 exceeds 10, and 5*5 > 10. 1 2 [4] [8] [5] [10] Row 24 = {9, 12, 16, 18, 24}, since numbers k such that rad(k) | 24 contains these numbers, furthermore, we have the following: 2 or 3 times 16 exceeds 24, 2 or 3 times 24 exceeds 24, 3*12 > 24, 2 or 3 times 18 exceeds 24, and 3*9 > 24. 1 2 4 8 [16] 3 6 [12] [24] [9] [18]
Links
- Michael De Vlieger, Table of n, a(n) for n = 2..11938 (rows n = 2..1000, flattened)
Programs
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Mathematica
(* First, run the "regs" function from A369609, then: *) Table[Select[regs[n], Function[k, AnyTrue[FactorInteger[n][[All, 1]], #*k > n &]]], {n, 2, 30}] // Flatten
Formula
For n in A000961, row n is {n}.
Comments