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A060683
Numbers for which the differences between consecutive divisors (ordered by size) are distinct.
20
1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 64, 65, 67, 68, 69, 71, 73, 74, 76, 77, 79, 81, 82, 83, 85, 86, 87, 88, 89, 92, 93, 94, 95, 97, 98
OFFSET
1,2
COMMENTS
A060682(a(n)) = A000005(a(n)) - 1, n > 1. - Reinhard Zumkeller, Jun 25 2015
LINKS
A. Balog, P. Erdős, and G. Tenenbaum, On Arithmetic Functions Involving Consecutive Divisors, In: Analytical Number Theory, pp. 77-90, Birkhäuser, Basel, 1990.
EXAMPLE
For n=6, divisors={1,2,3,6}; differences={1,1,3}, which are not distinct, so 6 is not in the sequence.
MATHEMATICA
test[n_ ] := Length[dd=Drop[d=Divisors[n], 1]-Drop[d, -1]]==Length[Union[dd]]; Select[Range[1, 100], test]
PROG
(Haskell)
a060683 n = a060683_list !! (n-1)
a060683_list = 1 : filter (\x -> a060682 x == a000005' x - 1) [2..]
-- Reinhard Zumkeller, Jun 25 2015
(PARI) isok(k) = my(d=divisors(k)); #Set(vector(#d-1, k, d[k+1]-d[k])) == #d-1; \\ Michel Marcus, Nov 11 2023
CROSSREFS
Cf. A060682, A259366 (complement).
Sequence in context: A091010 A306528 A116358 * A129511 A174905 A260402
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 19 2001
EXTENSIONS
Edited by Dean Hickerson, Jan 22 2002
STATUS
approved