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

Author

Labos Elemer, Apr 27 2001

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

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

Programs

Mathematica

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

PARI

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