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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 (list; graph; refs; listen; history; text; internal format)
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

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 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

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

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Last modified September 20 16:05 EDT 2017. Contains 292276 sequences.