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 A066241 1 + number of anti-divisors of n. 5

%I

%S 1,1,2,2,3,2,4,3,3,4,4,3,5,4,4,3,6,5,4,4,4,6,6,3,6,4,6,6,4,4,6,7,6,4,

%T 6,3,6,8,6,5,5,6,6,4,8,6,6,4,7,7,4,8,8,4,6,4,6,8,8,7,5,6,8,3,6,6,10,8,

%U 4,6,6,7,8,6,6,6,10,6,4,6,7,8,8,5,9,6,8,8,4,6,6,6,8,10,10,2,8,9,6,5

%N 1 + number of anti-divisors of n.

%C See A066272 for definition of anti-divisor.

%H Jon Perry, <a href="http://www.users.globalnet.co.uk/~perry/maths">Anti-divisors</a>

%H Jon Perry, <a href="/A066272/a066272a.html">The Anti-divisor</a> [Cached copy]

%H Jon Perry, <a href="/A066272/a066272.html">The Anti-divisor: Even More Anti-Divisors</a> [Cached copy]

%e For example, n = 18: 2n-1, 2n, 2n+1 are 35, 36, 37 with odd divisors > 1 {3,7,35}, {3,9}, {37} and quotients 7, 5, 1, 12, 4, 1, so the anti-divisors of 12 are 4, 5, 7, 12. Therefore a(18) = 1 + 4 = 5.

%t antid[n_] := Select[ Union[ Join[ Select[ Divisors[2n - 1], OddQ[ # ] && # != 1 &], Select[ Divisors[2n + 1], OddQ[ # ] && # != 1 &], 2n/Select[ Divisors[2*n], OddQ[ # ] && # != 1 &]]], # < n &]; Table[ Length[ antid[n]] + 1, {n, 1, 100} ]

%Y Cf. A058838. Equals 1 + A066272(n).

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_, Dec 31, 2001

%E More terms from _Robert G. Wilson v_, Jan 03 2002

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Last modified January 18 13:09 EST 2019. Contains 319271 sequences. (Running on oeis4.)