A060764 Number of divisors of n which are not also differences between consecutive divisors (ordered by increasing magnitude) of n.

1, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 3, 2, 2, 4, 1, 2, 3, 2, 2, 4, 2, 2, 4, 3, 2, 4, 2, 2, 4, 2, 1, 4, 2, 4, 4, 2, 2, 4, 4, 2, 4, 2, 2, 6, 2, 2, 5, 3, 3, 4, 2, 2, 4, 4, 4, 4, 2, 2, 5, 2, 2, 6, 1, 4, 4, 2, 2, 4, 5, 2, 6, 2, 2, 6, 2, 4, 4, 2, 5, 5, 2, 2, 7, 4, 2, 4, 2, 2, 6, 4, 2, 4, 2, 4, 6, 2, 3, 6, 3, 2, 4, 2, 2, 8

Offset: 1

Author

Labos Elemer, Apr 24 2001

Keywords

• nonn

Examples

			For n=70, divisors={1,2,5,7,10,14,35,70}; differences={1,3,2,3,4,21,35}; the divisors {5,7,10,14,70} are not differences, so a(70)=5.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000005, A060741, A060763.

Programs

Mathematica

a[n_] := Length[Complement[d=Divisors[n], Drop[d, 1]-Drop[d, -1]]]

PARI

A060764(n) = { my(divs=divisors(n), diffs=vecsort(vector(#divs-1,i,divs[i+1]-divs[i]), ,8), c=#divs); for(i=1,#diffs,if(!(n%diffs[i]),c--)); (c); }; \\ Antti Karttunen, Sep 21 2018

Python

from itertools import pairwise
from sympy import divisors
def A060764(n):
    e = map(lambda x:x[1]-x[0],pairwise(d:=divisors(n)))
    return len(set(d)-set(e)) # Chai Wah Wu, Feb 21 2023

Extensions

Edited by Dean Hickerson, Jan 22 2002