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A060798 Numbers n such that difference between upper and lower central divisors of n 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(n)-A060775(n)=1, where n=k*(k+1) and at least one of k and k+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

n = 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 n = 2^k(2^k-1) = 2^k*M or n = 2^k(2^k+1) = 2^k*F suitable M and F primes, then n is here (e.g., n = 272, 992, etc.). This holds also for n = 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: A243543 A094769 A068018 * A134320 A107383 A078025

Adjacent sequences:  A060795 A060796 A060797 * A060799 A060800 A060801

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 27 2001

STATUS

approved

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Last modified March 24 19:55 EDT 2017. Contains 283991 sequences.