

A324972


Squarefree polygonal numbers P(s,n) with s >= 3 and n >= 3.


4



6, 10, 15, 21, 22, 30, 33, 34, 35, 39, 42, 46, 51, 55, 57, 58, 65, 66, 69, 70, 78, 82, 85, 87, 91, 93, 94, 95, 102, 105, 106, 111, 114, 115, 118, 123, 129, 130, 133, 138, 141, 142, 145, 154, 155, 159, 165, 166, 174, 177, 178, 183, 185, 186, 190, 195, 201, 202
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OFFSET

1,1


COMMENTS

The main entry for this sequence is A090466 = polygonal numbers of order (or rank) greater than 2.
The special polygonal numbers A324973 form a subsequence that contains all Carmichael numbers A002997. See Kellner and Sondow 2019.


LINKS



FORMULA

Squarefree P(s,n) = (n^2*(s2)n*(s4))/2 with s >= 3 and n >= 3.


EXAMPLE

P(3,3) = 6 which is squarefree, so a(1) = 6.


MATHEMATICA

mx = 250; n = s = 3; lst = {};
While[s < Floor[mx/3] + 2, a = (n^2 (s  2)  n (s  4))/2;
If[a < mx + 1, AppendTo[lst, a], (s++; n = 2)]; n++]; lst = Union@lst;
Select[lst, SquareFreeQ]


PROG

(PARI) isok(n) = if (!issquarefree(n), return (0)); for(s=3, n\3+1, ispolygonal(n, s) && return(s)); \\ Michel Marcus, Mar 24 2019


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



