# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a290945 Showing 1-1 of 1 %I A290945 #18 Apr 22 2024 13:44:00 %S A290945 561,8911,10585,41041,115921,314821,334153,6313681,8134561,14913991, %T A290945 32914441,60957361,67902031,135556345,289766701,321197185,329769721, %U A290945 368113411,471905281,765245881,842202361,962442001,1507746241,2489462641,2588653081,3104207821 %N A290945 Triangular Carmichael numbers. %C A290945 Intersection of A000217 and A002997. %C A290945 The least triangular Carmichael numbers with the number of prime factors = 3, 4, 5, 6, 7, ... are: 561, 41041, 765245881, 321197185, 1583892181303201, ... %C A290945 The number of terms below 10^k for k = 3, 4, ... are: 1, 2, 4, 7, 9, 13, 22, 32, 53, 77, 137, 211, 358, 545, 879, 1423, ... %C A290945 Jonathan Vos Post discovered in 2004 that a(21) = 842202361 = A000217(41041) = A002817(286) is also a doubly triangular Carmichael number. The next number with this property is a(1108) = 292800629576356021 = A000217(765245881) = A002817(39121) (41041 and 765245881 are triangular Carmichael numbers that are also indices of triangular numbers that are also Carmichael numbers). %H A290945 Amiram Eldar, Table of n, a(n) for n = 1..8920 (terms below 10^22 calculated using data from Claude Goutier) %H A290945 Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22. %H A290945 Jonathan Vos Post, Table of Figurate Numbers, Sorted, Through 10,000. [Wayback Machine link] %H A290945 Index entries for sequences related to Carmichael numbers. %e A290945 8911 = A000217(133) = A002997(7) therefore 8911 is in the sequence. %t A290945 seqQ[n_]:=IntegerQ[Sqrt[8n+1]] && !PrimeQ[n] && (Mod[n, CarmichaelLambda[n]] == 1); Select[Range[10^6], seqQ] %Y A290945 Cf. A000217, A002817, A002997. %K A290945 nonn %O A290945 1,1 %A A290945 _Amiram Eldar_, Aug 14 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE