A195527 Integers n that are k-gonal for precisely 3 distinct values of k, where k >= 3.

15, 21, 28, 51, 55, 64, 70, 75, 78, 91, 96, 100, 111, 112, 117, 126, 135, 136, 141, 144, 145, 148, 154, 156, 165, 175, 176, 186, 189, 195, 201, 204, 216, 232, 235, 238, 246, 255, 256, 285, 286, 288, 291, 297, 300, 306, 315, 316, 321, 322, 324, 330, 333, 336

Offset: 1

Author

Ant King, Sep 21 2011

Keywords

• nonn

Comments

See A177025 for number of ways a number can be represented as a polygonal number.

Examples

			21 is in the sequence because it is a triangular number (A000217), an octagonal number (A000567) and an icosihenagonal number (A051873).
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A000567, A051873, A177025, A177029.

Programs

Mathematica

data1=Reduce[1/2 n (n(k-2)+4-k)== # && k>=3 && n>0, {k,n}, Integers]&/@Range[336]; data2=If[Head[#]===And, 1, Length[#]] &/@data1; data3=DeleteCases[Table[If[data2[[k]]==3, k], {k, 1, Length[data2]}], Null]

Python

A195527_list = []
for m in range(1,10**4):
    n, c = 3, 0
    while n*(n+1) <= 2*m:
        if not 2*(n*(n-2) + m) % (n*(n - 1)):
            c += 1
            if c > 2:
                break
        n += 1
    if c == 2:
        A195527_list.append(m) # Chai Wah Wu, Jul 28 2016