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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A177025 for number of ways a number can be represented as a polygonal number. LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 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 Cf. A000217, A000567, A051873, A177025, A177029. Sequence in context: A102030 A168104 A026048 * A047200 A070537 A324110 Adjacent sequences:  A195524 A195525 A195526 * A195528 A195529 A195530 KEYWORD nonn AUTHOR Ant King, Sep 21 2011 STATUS approved

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Last modified January 22 07:39 EST 2020. Contains 331139 sequences. (Running on oeis4.)