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A063778
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a(n) = the least integer that is polygonal in exactly n ways.
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15
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3, 6, 15, 36, 225, 561, 1225, 11935, 11781, 27405, 220780, 203841, 3368925, 4921840, 7316001, 33631521, 142629201, 879207616, 1383958576, 3800798001, 12524486976, 181285005825, 118037679760, 239764947345, 738541591425, 1289707733601, 1559439365121
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OFFSET
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1,1
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COMMENTS
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a(n) has exactly n representations as an m-gonal number P(m,r) = r*((m-2)*r-(m-4))/2, with m>2, r>1.
a(28) <= 14189300403201
a(29) <= 100337325689601
a(30) <= 1735471549713825
a(31) <= 334830950355825
a(32) <= 1473426934890625
a(33) <= 5409964920838401
(End)
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LINKS
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EXAMPLE
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a(3) = 15 because 15 is the least integer which is polygonal in 3 ways (15 is n-gonal for n = 3, 6, 15).
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MAPLE
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A063778 := proc(nmax) local a, n, ps ; a := [seq(0, i=1..nmax)] ; n := 1 ; while true do ps := A129654(n) ; if ps > 0 and ps <= nmax and n > 1 then if op(ps, a) = 0 then a := subsop(ps=n, a) ; print(a) ; fi ; fi ; n := n+1 ; end: RETURN(a) ; end: A063778(30) ; # R. J. Mathar, May 14 2007
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MATHEMATICA
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P[m_, r_] := P[m, r] = r*(4 + m*(r - 1) - 2*r)/2;
a[n_Integer] := a[n] = Module[{c, r, m, p, f}, p = 0; f = False; While[!f, p++; c = 0; For[m = 3, m <= p, m++, For[r = 1, r <= p, r++, If[p == P[m, r], c++; ]; ]; ]; If[c == n, f = True; ]; ]; p];
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PROG
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(PARI) lista(nn) = {rec = 0; for (n=3, nn, new = sum(k=3, n, ispolygonal(n, k)); if (new > rec, rec = new; print1(n, ", ")); ); } \\ Michel Marcus, Mar 25 2015
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CROSSREFS
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Cf. A177025 (number of different ways to represent n as a polygonal).
Cf. A129654 (number of different ways to represent n as general polygonal).
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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