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A333885 Number of triples (i,j,k) with 1 <= i < j < k <= n such that i divides j divides k. 1
0, 0, 0, 1, 1, 3, 3, 6, 7, 9, 9, 16, 16, 18, 20, 26, 26, 33, 33, 40, 42, 44, 44, 59, 60, 62, 65, 72, 72, 84, 84, 94, 96, 98, 100, 119, 119, 121, 123, 138, 138, 150, 150, 157, 164, 166, 166, 192, 193, 200, 202, 209, 209, 224, 226, 241, 243, 245, 245, 276, 276 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Sum_{m=1..n} Sum_{d|m, d<m} (tau(d)-1). - Alois P. Heinz, Apr 09 2020

EXAMPLE

The a(4) = 1 triple is (1,2,4).

The a(8) = 6 triples are (1,2,4), (1,2,6), (1,2,8), (1,3,6), (1,4,8), (2,4,8).

MAPLE

with(numtheory):

a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+

       add(tau(d)-1, d=divisors(n) minus {n}))

    end:

seq(a(n), n=1..80);  # Alois P. Heinz, Apr 09 2020

MATHEMATICA

a[n_] := a[n] = If[n == 0, 0, a[n - 1] + Sum[DivisorSigma[0, d] - 1, {d, Most @ Divisors[n]}]];

Array[a, 80] (* Jean-Fran├žois Alcover, Nov 27 2020, after Alois P. Heinz *)

PROG

(Python) an = len([(i, j, k) for i in range(1, n+1) for j in range(i+1, n+1) for k in range(j+1, n+1) if j%i==0 and k%j==0])

CROSSREFS

Cf. A000005, A002541, A320224.

Sequence in context: A273062 A269170 A003879 * A270060 A350636 A078565

Adjacent sequences:  A333882 A333883 A333884 * A333886 A333887 A333888

KEYWORD

nonn

AUTHOR

Derek Lim, Apr 08 2020

STATUS

approved

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Last modified May 24 00:15 EDT 2022. Contains 353993 sequences. (Running on oeis4.)