A177029 Numbers that have exactly two different representations as polygonal numbers.

6, 9, 10, 12, 16, 18, 22, 24, 25, 27, 30, 33, 34, 35, 39, 40, 42, 46, 48, 49, 52, 54, 57, 58, 60, 63, 65, 69, 72, 76, 82, 84, 85, 87, 88, 90, 92, 93, 94, 95, 99, 102, 106, 108, 114, 115, 118, 121, 123, 124, 125, 129, 130, 132, 133, 138, 142, 147, 150, 155, 159, 160, 162, 166, 168

Offset

1,1

Comments

Numbers that have only A177025(.)=1 representation are listed by A090467.

Links

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

Formula

{m: A177025(m)=2}.

Example

6 is a triangular and a hexagonal number, but is not any other k-gonal number.

Prog

(PARI) lista(nn) = {for (n=1, nn, if (sum(k=3, n, ispolygonal(n, k)) == 2, print1(n, ", ")); ); } \\ Michel Marcus, Mar 25 2015
(Python)
A177029_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 > 1:
                break
        n += 1
    if c == 1:
        A177029_list.append(m) # Chai Wah Wu, Jul 28 2016

Crossrefs

Cf. A177025, A090467, A177028, A000217, A000326, A000384, A000566, A000567, A176949, A176948, A176774, A176744, A176747, A176775, A175873, A176874.

Sequence in context: A039725 A262362 A125494 * A105066 A048283 A169692

Adjacent sequences: A177026 A177027 A177028 * A177030 A177031 A177032

Keyword

nonn

Author

Vladimir Shevelev, May 01 2010

Extensions

Extended by R. J. Mathar, Aug 15 2010

Status

approved