来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a324320 Showing 1-1 of 1 %I A324320 %S A324320 1045,2465,2821,15841,20501,34133,51221,68101,89441,116033,118405, %T A324320 162401,170885,216545,300833,364705,439301,472033,530881,642181, %U A324320 687365,746005 %N A324320 Terms of A324315 (squarefree integers m > 1 such that if prime p divides m, then the sum of the base p digits of m is at least p) that are also octagonal numbers (A000567) with index equal to their largest prime factor. %C A324320 2465 is also a Carmichael number (A002997). %C A324320 2821 is also a primary Carmichael number (A324316). %C A324320 See the section on polygonal numbers in Kellner and Sondow 2019. %C A324320 Subsequence of the special polygonal numbers A324973. -乔纳森桑多维,3月27日2019,%A324320 Bernd C. Kellner和Jonathan Sondow,幂和分母,阿梅尔。数学月,124(2017),695-709。DOI:104169/A.M.th.L.124.8695,阿西夫:一千七百零五点零三八五七%H A324320 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 [math.NT] 2019. %e A324320 A324315(4) = 1045 = 5 * 11 * 19 = 19 * (3 * 19 - 2) = A000567(19), so 1045 is a member. %t A324320 SD[n_, p_] := If[n < 1 || p < 2, 0, Plus @@ IntegerDigits[n, p]]; %t A324320 LP[n_] := Transpose[FactorInteger[n]][[1]]; %t A324320 ON[n_] := n(3n - 2); %t A324320 TestS[n_] := (n > 1) && SquareFreeQ[n] && VectorQ[LP[n], SD[n, #] >= # &]; %t A324320 Select[ON@ Prime[Range[100]], TestS[#] &] %Y A324320 Cf. A000567, A002997, A324315, A324316, A324317, A324318, A324319, A324369, A324370, A324371, A324404, A324405, A324973. %K A324320 nonn,base %O A324320 1,1 %A A324320 _Bernd C. Kellner_ and _Jonathan Sondow_, Feb 23 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE