A060794 Difference between upper and lower central divisors of n.

1, 2, 1, 4, 1, 6, 2, 2, 3, 10, 1, 12, 5, 2, 2, 16, 3, 18, 1, 4, 9, 22, 2, 4, 11, 6, 3, 28, 1, 30, 4, 8, 15, 2, 2, 36, 17, 10, 3, 40, 1, 42, 7, 4, 21, 46, 2, 6, 5, 14, 9, 52, 3, 6, 1, 16, 27, 58, 4, 60, 29, 2, 4, 8, 5, 66, 13, 20, 3, 70, 1, 72, 35, 10, 15, 4, 7, 78, 2, 6, 39, 82, 5, 12, 41, 26

Offset

2,2

Links

Harry J. Smith, Table of n, a(n) for n = 2..1000

Example

Difference between upper and lower central divisors may be small or relatively large. So neither A060775 nor A033677 are always good central divisors as to their magnitude. n=182,D={1,2,7,13,14,26,91,182}; central divisors={13,14}, difference=1. n=254, D={1,2,127,254}, central divisors={2,127}, a(254)=125. n=p, D={1,p}. Here the central divisors are also marginal ones: a(p)=p-1.

Mathematica

a(n)=Part[Divisors[n], 1+cd[n]]-Part[Divisors[n], cd[n]], where cd[x_] := cd[x_] := Floor[DivisorSigma[0, x]/2]

Prog

(PARI) a(n)={my(d=divisors(n)); if(n>1, d[1 + #d\2] - d[#d\2], 0)} \\ Harry J. Smith, Jul 12 2009

Crossrefs

a(n) = A033677(n) - A060775(n).

Cf. A060775, A060776, A060777, A033677, A000196.

Sequence in context: A176729 A300509 A074643 * A300716 A074919 A362232

Adjacent sequences: A060791 A060792 A060793 * A060795 A060796 A060797

Keyword

nonn

Author

Labos Elemer, Apr 27 2001

Status

approved