The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A080765 Integers m such that m+1 divides lcm(1 through m). 10
 5, 9, 11, 13, 14, 17, 19, 20, 21, 23, 25, 27, 29, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 47, 49, 50, 51, 53, 54, 55, 56, 57, 59, 61, 62, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 101, 103, 104, 105, 107 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Integers m for which A003418(m) = A003418(m+1). a(n) = A024619(n) - 1. Proof: If N+1 is a power of a prime (N+1=P^K), then only smaller powers of that prime divide numbers up to N and so lcm(1..N) doesn't have K powers of P; that is, N+1=P^K doesn't divide lcm(1..N). From Don Reble, Mar 12 2003: (Start) If N+1 is not a power of a prime, then it has at least two prime factors. Call one of them P, let K be such that P^K divides N+1, but P^(K+1) doesn't, and let N+1=P^K*R. Then - R is greater than 1 because it is divisible by another prime factor of N+1; - P^K and R are each less than N+1 because the other is greater than one; - lcm(P^K,R) divides lcm(1..N) because 1..N includes both numbers; - lcm(P^K,R)=N+1 because P doesn't divide R; - N+1 divides lcm(1..N). (End) LINKS David A. Corneth, Table of n, a(n) for n = 1..10000 Andrei Asinowski, Cyril Banderier, Benjamin Hackl, Flip-sort and combinatorial aspects of pop-stack sorting, arXiv:2003.04912 [math.CO], 2020. FORMULA a(n) ~ n. - David A. Corneth, Aug 30 2019 EXAMPLE 17 is the sequence because lcm(1,2,...,17)=12252240 and 17+1=18 divides 12252240. MATHEMATICA Select[Range, Divisible[LCM @@ Range[#], #+1]&] (* Jean-François Alcover, Jun 21 2018 *) PROG (PARI) a=1; for(n=1, 108, a=lcm(a, n); if(a%(n+1)==0, print1(n, ", "))) \\ Klaus Brockhaus, Jun 11 2004 (PARI) first(n) = {my(u = max(2*n, 50), charact = vector(u, i, 1), res = List()); forprime(p = 2, 2*n, for(t = 1, logint(u, p), charact[p^t - 1] = 0)); for(i = 1, u, if(charact[i] == 1, listput(res, i); if(#res >= n, return(res)))); res } \\ David A. Corneth, Aug 30 2019 (Sage) [x - 1 for x in (1..108) if not is_prime_power(n)]  # Peter Luschny, May 23 2013 CROSSREFS Cf. A003418. Sequence in context: A049049 A118358 A101731 * A226039 A257292 A234285 Adjacent sequences:  A080762 A080763 A080764 * A080766 A080767 A080768 KEYWORD nonn,easy AUTHOR Lekraj Beedassy, Mar 10 2003 EXTENSIONS More terms from Klaus Brockhaus, Jun 11 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 30 20:11 EDT 2020. Contains 338090 sequences. (Running on oeis4.)