

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
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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(n1) + a(n2).  Georgi Guninski, Jun 07 2010
Empirical g.f.: (2*x^22*x+1)*(x^3x^2x1) / (x1)^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^j1) = 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



