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%I #10 Jul 28 2016 21:16:02
%S 36,45,66,81,105,120,153,171,190,196,210,261,280,351,378,396,400,405,
%T 406,456,465,477,484,496,532,576,585,606,621,630,645,666,715,726,729,
%U 736,741,742,765,780,784,801,855,876,891,910,945,960,981,1015,1045,1056
%N Integers n that are k-gonal for precisely 4 distinct values of k, where k >= 3.
%C See A177025 for number of ways a number can be represented as a polygonal number.
%H Chai Wah Wu, <a href="/A195528/b195528.txt">Table of n, a(n) for n = 1..10000</a>
%e 36 is in the sequence because it is a triangular number (A000217), a square number (A000290), a tridecagonal number (A051865), and a 36-gonal number.
%t data1=Reduce[1/2 n (n(k-2)+4-k)==# && k>=3 && n>0, {k,n}, Integers]&/@Range[1056]; data2=If[Head[#]===And, 1, Length[#]] &/@data1; data3=DeleteCases[Table[If[data2[[k]]==4, k], {k, 1, Length[data2]}], Null]
%o (Python)
%o A195528_list = []
%o for m in range(1,10**4):
%o n, c = 3, 0
%o while n*(n+1) <= 2*m:
%o if not 2*(n*(n-2) + m) % (n*(n - 1)):
%o c += 1
%o if c > 3:
%o break
%o n += 1
%o if c == 3:
%o A195528_list.append(m) # _Chai Wah Wu_, Jul 28 2016
%Y Cf. A000217, A000290, A051865, A177025, A177029.
%K nonn
%O 1,1
%A _Ant King_, Sep 21 2011
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