OFFSET
1,1
COMMENTS
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) > 4*10^12. - Donovan Johnson, Dec 08 2010
From Husnain Raza, Jan 01 2024: (Start)
a(28) <= 14189300403201
a(29) <= 100337325689601
a(30) <= 1735471549713825
a(31) <= 334830950355825
a(32) <= 1473426934890625
a(33) <= 5409964920838401
(End)
LINKS
Eric Weisstein's World of Mathematics, Polygonal Number.
EXAMPLE
a(3) = 15 because 15 is the least integer which is polygonal in 3 ways (15 is n-gonal for n = 3, 6, 15).
MAPLE
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
MATHEMATICA
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];
Table[a[n], {n, 1, 5}] (* Robert P. P. McKone, Jan 02 2024 *)
PROG
(PARI) a(n) = my(k=3); while (sum(p=3, k, ispolygonal(k, p)) != n, k++); k; \\ Michel Marcus, Aug 17 2024
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
David W. Wilson, Aug 16 2001
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 23 2007
a(22)-a(27) from Donovan Johnson, Dec 08 2010
STATUS
approved