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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 (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 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 Cf. A000217, A000290, A051865, A177025, A177029. Sequence in context: A250641 A168107 A048034 * A144291 A068143 A264961 Adjacent sequences:  A195525 A195526 A195527 * A195529 A195530 A195531 KEYWORD nonn AUTHOR Ant King, Sep 21 2011 STATUS approved

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Last modified April 13 03:43 EDT 2021. Contains 342934 sequences. (Running on oeis4.)