来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a324316 Showing 1-1 of 1 %I A324316 %S A324316 1729,2821,29341,46657,252601,294409,399001,488881,512461,1152271, %T A324316 1193221,1857241,3828001,4335241,5968873,6189121,6733693,6868261, %U A324316 7519441,10024561,10267951,10606681,14469841,14676481,15247621,15829633,17098369,17236801,17316001,19384289,23382529,29111881,31405501,34657141,35703361,37964809 %N A324316 Primary Carmichael numbers. %C A324316 Squarefree integers m > 1 such that if prime p divides m, then the sum of the base-p digits of m equals p. It follows that m is then a Carmichael number (A002997). %C A324316 Conjecture: the sequence is infinite. %C A324316 If m is a term and p is a prime factor of m, then p <= a*sqrt(m) with a = sqrt(66337/132673) = 0.7071..., where the bound is sharp. %C A324316 The distribution of primary Carmichael numbers is A324317. %C A324316 See Kellner and Sondow 2019 and Kellner 2019. %C A324316 Primary Carmichael numbers are special polygonal numbers A324973. 第n次Ca迈克尔数的秩是A32497(n)。见凯尔纳和索道2019。-乔纳森桑多维,3月26日2019岁%A324316 Bernd C. Kellner,n,a(n)n=1…10000的表(通过使用PiCH的数据库计算,见下面的链接)%%A324316 Bernd C. Kellner和Jonathan Sondow,幂和分母阿梅尔。数学月,124(2017),695-709;ARXIV:一千七百零五点零三八五七[Maun.NT],2017 .%%H A324316 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 A324316 Bernd C. Kellner,关于初等Carmichael数,ARXIV:1902.11283 [数学,NT ],2019。卡迈克尔数高达10 ^ 18,2008。%H H A324316与卡迈克尔数相关的序列的索引条目。%F A324316 AA1+AY2+…如果p为素数,m=Ay1*P+Ay2*P^ 2+,则+Ayk= p。+ a_k * p^k with 0 <= a_i <= p-1 for i = 1, 2, ..., k (note that a_0 = 0). %e A324316 1729 = 7 * 13 * 19 is squarefree, and 1729 in base 7 is 5020_7 = 5 * 7^3 + 0 * 7^2 + 2 * 7 + 0 with 5+0+2+0 = 7, and 1729 in base 13 is a30_13 with a+3+0 = 10+3+0 = 13, and 1729 in base 19 is 4f0_19 with 4+f+0 = 4+15+0 = 19, so 1729 is a member. %t A324316 SD[n_, p_] := If[n < 1 || p < 2, 0, Plus @@ IntegerDigits[n, p]]; %t A324316 LP[n_] := Transpose[FactorInteger[n]][[1]]; %t A324316 TestCP[n_] := (n > 1) && SquareFreeQ[n] && VectorQ[LP[n], SD[n, #] == # &]; %t A324316 Select[Range[1, 10^7, 2], TestCP[#] &] %o A324316 (Perl) use ntheory ":all"; my $m; forsquarefree { $m=$_; say if @_ > 2 && is_carmichael($m) && vecall { $_ == vecsum(todigits($m,$_)) } @_; } 1e7; # _Dana Jacobsen_, Mar 28 2019 %Y A324316 Subsequence of A002997, A324315. %Y A324316 Least primary Carmichael number with n prime factors is A306657. %Y A324316 Cf. also A005117, A195441, A324317, A324318, A324319, A324320, A324369, A324370, A324371, A324404, A324405,A32493,A32497 6 .0%K A324316 NON,基础%%A324316,1,1%A324316.BELND C.KELNELNY和JONATAN SONDOWAY,2月21日2019μl内容在OEIS最终用户许可协议下可用:HTTP:/OEIS.Org/许可证