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A060794 Difference between upper and lower central divisors of n. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A138009

Adjacent sequences:  A060791 A060792 A060793 * A060795 A060796 A060797

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 27 2001

STATUS

approved

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Last modified May 11 11:54 EDT 2021. Contains 343791 sequences. (Running on oeis4.)