login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A060798 Numbers k such that difference between upper and lower central divisors of k is 1. 1
1, 2, 4, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, 2450 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

FORMULA

Solutions to A033677(k) - A060775(k) = 1, where k = j*(j+1) and at least one of j and j+1 is composite.

Except at n < 5, this sequence seems to satisfy a(n+1) = 3*a(n) - 3*a(n-1) + a(n-2). - Georgi Guninski, Jun 07 2010

Empirical g.f.: (2*x^2-2*x+1)*(x^3-x^2-x-1) / (x-1)^3. - Colin Barker, Apr 16 2014

EXAMPLE

k = 4032 = 2*2*2*2*2*2*3*3*7 is here because its central (the 21st and 22nd) divisors are {63,64} with difference = 1. If k = 2^j(2^j-1) = 2^j*M or k = 2^j(2^j+1) = 2^j*F suitable M and F primes, then k is here (e.g., k = 272, 992, etc.). This holds also for k = C*(C+1) products where C is composite and C+1 is prime, e.g., C = 2310.

PROG

(PARI) { n=-1; for (m=1, 999000, d=divisors(m); if (m==1 || (d[1 + length(d)\2] - d[length(d)\2]) == 1, write("b060798.txt", n++, " ", m)); ) } \\ Harry J. Smith, Jul 13 2009

CROSSREFS

Cf. A000196, A033677, A060775.

Sequence in context: A094769 A068018 A294918 * A134320 A294430 A294429

Adjacent sequences:  A060795 A060796 A060797 * A060799 A060800 A060801

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 27 2001

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 18 14:15 EST 2017. Contains 294893 sequences.