cp's OEIS Frontend

A195528 Integers n that are k-gonal for precisely 4 distinct values of k, where k >= 3.

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