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A177029 Numbers that have exactly two different representations as polygonal numbers. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 21 04:27 EDT 2017. Contains 289632 sequences.