A060764 - OEIS

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

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OFFSET

1,3

LINKS

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

EXAMPLE

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.

MATHEMATICA

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

PROG

(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

CROSSREFS

Cf. A000005, A060741, A060763.

Sequence in context: A318874 A001227 A369466 * A105149 A355748 A295894

Adjacent sequences: A060761 A060762 A060763 * A060765 A060766 A060767

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 24 2001

EXTENSIONS

Edited by Dean Hickerson, Jan 22 2002

STATUS

approved