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A195527
Integers n that are k-gonal for precisely 3 distinct values of k, where k >= 3.
7
15, 21, 28, 51, 55, 64, 70, 75, 78, 91, 96, 100, 111, 112, 117, 126, 135, 136, 141, 144, 145, 148, 154, 156, 165, 175, 176, 186, 189, 195, 201, 204, 216, 232, 235, 238, 246, 255, 256, 285, 286, 288, 291, 297, 300, 306, 315, 316, 321, 322, 324, 330, 333, 336
OFFSET
1,1
COMMENTS
See A177025 for number of ways a number can be represented as a polygonal number.
EXAMPLE
21 is in the sequence because it is a triangular number (A000217), an octagonal number (A000567) and an icosihenagonal number (A051873).
MATHEMATICA
data1=Reduce[1/2 n (n(k-2)+4-k)== # && k>=3 && n>0, {k, n}, Integers]&/@Range[336]; data2=If[Head[#]===And, 1, Length[#]] &/@data1; data3=DeleteCases[Table[If[data2[[k]]==3, k], {k, 1, Length[data2]}], Null]
PROG
(Python)
A195527_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 > 2:
break
n += 1
if c == 2:
A195527_list.append(m) # Chai Wah Wu, Jul 28 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Ant King, Sep 21 2011
STATUS
approved