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A177201 Multiples of nontrivially polygonal numbers A090466. 1

%I #6 Sep 15 2013 00:56:00

%S 6,9,10,12,15,16,18,20,21,22,24,25,27,28,30,32,33,34,35,36,39,40,42,

%T 44,45,46,48,49,50,51,52,54,55,56,57,58,60,63,64,65,66,68,69,70,72,75,

%U 76,78,80,81,82,84,85,87,88,90,91,92,93,94,95,96,98,99,100

%N Multiples of nontrivially polygonal numbers A090466.

%C Multiples of numbers in the array of A057145 below the second row (which has every positive integer) and right of the 2nd column (which has every positive integer). That is, multiples of every triangular number >3, every square >4, every pentagonal number >5, every hexagonal number >6, every heptagonal number >7, every octagonal number >8, every 9-gonal (nonagonal) number >9, and so forth.

%C Nontrivially polygonal numbers {6, 9, 10, 12, 15, 16, 18, 21, 22, 24, 25, 27, 28, 30, 33, 34, 35, 36, 39, 40, 42, 45, 46, 48, 49,...} UNION 2*nontrivially polygonal = {12, 18, 20, 24, 30, 32, 36, 42, 44, 48, 50, 54, 56, 60, 66, 68, 70, 72, 78, 80, 84, 90, 92, 96, 98, ...} UNION 3*nontrivially polygonal = {18, 27, 30, 36, 45, 48, 54, 63, 66, 72, 75, 81, 84, 90, 99, ...} UNION 4*nontrivially polygonal = {24, 36, 40, 48, 60, 64, 72, 84, 88, 96, 100, ...} UNION 5*nontrivially polygonal = {30, 45, 50, 60, 75, 80, 90, ...} UNION 6*nontrivially polygonal = {36, 54, 60, 72, 90, 96, ...} UNION 7*nontrivially polygonal = {42, 63, 70, 84, ...} and so forth.

%F {A057145 * j for j = 1, 2, 3, 4, 5, ...} = {j * ((n-2)*k^2-(n-4)*k)/2, j>0, n > 2, k > 2}.

%Y Cf. A057145, A090466, complement is A177202.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, May 04 2010

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