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A066241 1 + number of anti-divisors of n. 5
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A066272 for definition of anti-divisor.

LINKS

Table of n, a(n) for n=1..100.

Jon Perry, Anti-divisors

Jon Perry, The Anti-divisor [Cached copy]

Jon Perry, The Anti-divisor: Even More Anti-Divisors [Cached copy]

EXAMPLE

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.

MATHEMATICA

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} ]

CROSSREFS

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

Sequence in context: A107324 A023522 A205000 * A060025 A067399 A106737

Adjacent sequences:  A066238 A066239 A066240 * A066242 A066243 A066244

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 31, 2001

EXTENSIONS

More terms from Robert G. Wilson v, Jan 03 2002

STATUS

approved

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Last modified October 16 12:35 EDT 2018. Contains 316263 sequences. (Running on oeis4.)