来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a324973 Showing 1-1 of 1 %I A324973 %S A324973 6,15,66,70,91,190,231,435,561,703,715,782,861,946,1045,1105,1426, %T A324973 1653,1729,1770,1785,1794,1891,2035,2278,2465,2701,2821,2926,3059, %U A324973 3290,3367,3486,3655,4371,4641,4830,5083,5365,5551,5565,6601,7337,7526,8029,8170,8695 %N A324973 Special polygonal numbers. %C A324973 Squarefree polygonal numbers P(r,p) = (p^2*(r-2)-p*(r-4))/2 whose greatest prime factor is p >= 3, and whose rank (or order) is r >= 3 (see A324974). %C A324973 The Carmichael numbers A002997 and primary Carmichael numbers A324316 are subsequences. 见凯尔纳和索道2019。%%H A32493 Bernd C. Kellner和Jonathan Sondow,关于CalMekes和多边形数、伯努利多项式和Base-P数字的和,ARXIV:1902.10672 [数学,NT ],2019。%%H A32493维基百科,多边形数%e A324973 P(3,5) = 15 is squarefree, and its greatest prime factor is 5, so 15 is a member. %e A324973 More generally, if p is an odd prime and P(3,p) is squarefree, then P(3,p) is a member, since P(3,p) = (p^2+p)/2 = p*(p+1)/2, so p is its greatest prime factor. %e A324973 CAUTION: P(6,7) = 91 = 7*13 is a member even though 7 is NOT its greatest prime factor, as P(6,7) = P(3,13) and 13 is its greatest prime factor. %t A324973 GPF[n_] := Last[Select[Divisors[n], PrimeQ]]; %t A324973 T = Select[Flatten[Table[{p, (p^2*(r - 2) - p*(r - 4))/2}, {p, 3, 100}, {r, 3, 40}], 1], SquareFreeQ[Last[#]] && First[#] == GPF[Last[#]] &]; %t A324973 Take[Union[Table[Last[t], {t, T}]], 47] %Y A324973 Subsequence of A324972 = intersection of A005117 and A090466. %Y A324973 A002997, A324316, A324319 and A324320 are subsequences. %Y A324973 Cf. also A324974, A324975, A324976. %K A324973 nonn %O A324973 1,1 %A A324973 _Bernd C. Kellner_ and _Jonathan Sondow_, 3月21日在OEIS终端用户许可协议下可用的2019μl内容:HTTP:/OEIS.Org/许可证