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

1,2

Comments

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

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.

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. A000005, A060680, A060681, A060682, A060765.

Cf. A060682, A259366 (complement).

Sequence in context: A091010 A306528 A116358 * A129511 A174905 A260402

Adjacent sequences: A060680 A060681 A060682 * A060684 A060685 A060686

Keyword

nonn

Author

Labos Elemer, Apr 19 2001

Extensions

Edited by Dean Hickerson, Jan 22 2002

Status

approved