A195528 - OEIS

%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