

A063778


a(n) = the least integer that is polygonal in exactly n ways.


4



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

1,1


COMMENTS

a(n) has exactly n representations as an mgonal number P(m,r) = r*((m2)*r(m4))/2, with m>2, r>1.
a(28) > 4*10^12.  Donovan Johnson, Dec 08 2010


LINKS

Table of n, a(n) for n=1..27.
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 ngonal 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


PROG

(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


CROSSREFS

Cf. A177025 (number of different ways to represent n as a polygonal).
Cf. A129654 (number of different ways to represent n as general polygonal).
Sequence in context: A005043 A099323 A058534 * A279374 A087124 A086326
Adjacent sequences: A063775 A063776 A063777 * A063779 A063780 A063781


KEYWORD

nonn,nice


AUTHOR

David W. Wilson, Aug 16 2001


EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of Andrew Plewe, May 23 2007
a(22)a(27) from Donovan Johnson, Dec 08 2010


STATUS

approved



