A275256 Numbers with a minimum of 6 polygonal roots, excluding itself.

1225, 1540, 2926, 4005, 5985, 8856, 9045, 9801, 11781, 11935, 12376, 12496, 12720, 13041, 14400, 16401, 17200, 17226, 17290, 17865, 18096, 21528, 21736, 23001, 23751, 24220, 24976, 25425, 26796, 27000, 27405, 27951, 29241, 29316, 29601, 29646, 30976, 31465, 31536

Offset: 1

Author

Matthew Parker, Jul 21 2016

Keywords

• nonn

Comments

The i-th k-gonal number is equal to ((k-2)*i^2-(k-4)*i)/2. Sequence lists numbers n which are k-gonal numbers with k < n in at least 6 ways. - N. J. A. Sloane, Jul 25 2016

All polygonal roots (R) can be calculated for each number by checking if any numbers less than N give an integer result from (((K - 2) * (N * N) - (K - 4) * N) / 2), where K is increased until the numbers returned are larger than our N.

Examples

			For n = 5 we have a(5) = 5985. 5985 has 6 polygonal roots, since 5985 is the 45th octagonal number, the 35th dodecagonal number, the 18th 41-gonal number, the 9th 168-gonal number, the fifth 600-gonal number, and the third 1996-gonal number.
		

Links

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

Programs

Python

A275256_list = []
for m in range(2,10**5):
    n, c = 3, 0
    while (n*(n+1)) <= 2*m:
        if not 2*(n*(n-2) + m) % (n*(n - 1)):
            c += 1
            if c >= 6:
                break
        n += 1
    if c >= 6:
        A275256_list.append(m) # Chai Wah Wu, Jul 25 2016

Extensions

a(22)-a(39) from Chai Wah Wu, Jul 24 2016