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

36, 45, 66, 81, 105, 120, 153, 171, 190, 196, 210, 261, 280, 351, 378, 396, 400, 405, 406, 456, 465, 477, 484, 496, 532, 576, 585, 606, 621, 630, 645, 666, 715, 726, 729, 736, 741, 742, 765, 780, 784, 801, 855, 876, 891, 910, 945, 960, 981, 1015, 1045, 1056

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

			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.
		

Links

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

Crossrefs

Cf. A000217, A000290, A051865, A177025, A177029.

Programs

Mathematica

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]

Python

A195528_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 > 3:
                break
        n += 1
    if c == 3:
        A195528_list.append(m) # Chai Wah Wu, Jul 28 2016