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A195528
Integers n that are k-gonal for precisely 4 distinct values of k, where k >= 3.
7
36, 45, 66, 81, 105, 120, 153, 171, 190, 196, 210, 261, 280, 351, 378, 396, 400, 405, 406, 456, 465, 477, 484, 496, 532, 576, 585, 606, 621, 630, 645, 666, 715, 726, 729, 736, 741, 742, 765, 780, 784, 801, 855, 876, 891, 910, 945, 960, 981, 1015, 1045, 1056
OFFSET
1,1
COMMENTS
See A177025 for number of ways a number can be represented as a polygonal number.
EXAMPLE
36 is in the sequence because it is a triangular number (A000217), a square number (A000290), a tridecagonal number (A051865), and a 36-gonal number.
MATHEMATICA
data1=Reduce[1/2 n (n(k-2)+4-k)==# && k>=3 && n>0, {k, n}, Integers]&/@Range[1056]; data2=If[Head[#]===And, 1, Length[#]] &/@data1; data3=DeleteCases[Table[If[data2[[k]]==4, k], {k, 1, Length[data2]}], Null]
PROG
(Python)
A195528_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 > 3:
break
n += 1
if c == 3:
A195528_list.append(m) # Chai Wah Wu, Jul 28 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Ant King, Sep 21 2011
STATUS
approved