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A177029
Numbers that have exactly two different representations as polygonal numbers.
11
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.
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
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, May 01 2010
EXTENSIONS
Extended by R. J. Mathar, Aug 15 2010
STATUS
approved