A060683 Numbers for which the differences between consecutive divisors (ordered by size) are distinct.

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

Author

Labos Elemer, Apr 19 2001

Keywords

• nonn

Comments

A060682(a(n)) = A000005(a(n)) - 1, n > 1. - Reinhard Zumkeller, Jun 25 2015

Examples

			For n=6, divisors={1,2,3,6}; differences={1,1,3}, which are not distinct, so 6 is not in the sequence.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• A. Balog, P. Erdős, and G. Tenenbaum, On Arithmetic Functions Involving Consecutive Divisors, In: Analytical Number Theory, pp. 77-90, Birkhäuser, Basel, 1990.

Crossrefs

Cf. A000005, A060680, A060681, A060682, A060765.

Cf. A060682, A259366 (complement).

Programs

Haskell

a060683 n = a060683_list !! (n-1)
a060683_list = 1 : filter (\x -> a060682 x == a000005' x - 1) [2..]
-- Reinhard Zumkeller, Jun 25 2015

Mathematica

test[n_ ] := Length[dd=Drop[d=Divisors[n], 1]-Drop[d, -1]]==Length[Union[dd]]; Select[Range[1, 100], test]

PARI

isok(k) = my(d=divisors(k)); #Set(vector(#d-1, k, d[k+1]-d[k])) == #d-1; \\ Michel Marcus, Nov 11 2023

Extensions

Edited by Dean Hickerson, Jan 22 2002