The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A059267 Numbers n with 2 divisors d1 and d2 having difference 2: d2 - d1 = 2; equivalently, numbers that are 0 (mod 4) or have a divisor d of the form d = m^2 - 1. 5
 3, 4, 6, 8, 9, 12, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 51, 52, 54, 56, 57, 60, 63, 64, 66, 68, 69, 70, 72, 75, 76, 78, 80, 81, 84, 87, 88, 90, 92, 93, 96, 99, 100, 102, 104, 105, 108, 111, 112, 114, 116, 117, 120, 123, 124, 126, 128 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Complement of A099477; A008586, A008585 and A037074 are subsequences - Reinhard Zumkeller, Oct 18 2004 These numbers have an asymptotic density of ~ 0.522. This corresponds to all numbers which are multiples of 4 (25%), or of 3 (having 1 & 3 as divisors: + (1-1/4)*1/3 = 1/4), or of 5*7, or of 11*13, etc. (Generally, multiples of lcm(k,k+2), but multiples of 3 and 4 are already taken into account in the 50% covered by the first 2 terms.) - M. F. Hasler, Jun 02 2012 By considering divisors of the form m^2-1 with m <= 200 it is possible to prove that the density of this sequence is in the interval (0.5218, 0.5226). The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 5, 52, 521, 5219, 52206, 522146, 5221524, 52215473, 522155386, 5221555813, ..., so the asymptotic density of this sequence can be estimated empirically by 0.522155... . - Amiram Eldar, Sep 25 2022 LINKS M. F. Hasler, Table of n, a(n) for n = 1..3131 FORMULA A099475(a(n)) > 0. - Reinhard Zumkeller, Oct 18 2004 EXAMPLE a(18) = 35 because 5 and 7 divide 35 and 7 - 5 = 2. MAPLE with(numtheory): for n from 1 to 1000 do flag := 1: if n mod 4 = 0 then printf(`%d, `, n):flag := 0 fi: for m from 2 to ceil(sqrt(n)) do if n mod (m^2-1) = 0 and flag=1 then printf(`%d, `, n); break fi: od: od: MATHEMATICA d1d2Q[n_]:=Mod[n, 4]==0||AnyTrue[Sqrt[#+1]&/@Divisors[n], IntegerQ]; Select[ Range[ 200], d1d2Q] (* Harvey P. Dale, May 31 2020 *) PROG (PARI) isA059267(n)={ n%4==0 || fordiv( n, d, issquare(d+1) && return(1))} \\ M. F. Hasler, Aug 29 2008 (PARI) is_A059267(n) = fordiv( n, d, n%(d+2)||return(1)) \\ M. F. Hasler, Jun 02 2012 CROSSREFS Cf. A099475, A099477, A008585, A008586, A037074. Sequence in context: A192519 A036446 A284469 * A355200 A049433 A250984 Adjacent sequences: A059264 A059265 A059266 * A059268 A059269 A059270 KEYWORD nonn AUTHOR Avi Peretz (njk(AT)netvision.net.il), Jan 23 2001 EXTENSIONS More terms from James A. Sellers, Jan 24 2001 Removed comments linking to A143714, which seem wrong, as observed by Ignat Soroko, M. F. Hasler, Jun 02 2012 STATUS approved

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

Last modified March 25 03:32 EDT 2023. Contains 361511 sequences. (Running on oeis4.)