OFFSET
1,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
EXAMPLE
The number of divisors of the integers 1 through 10 form the sequence 1,2,2,3,2,4,2,4,3,4. The divisors of 10 are 1,2,5,10. The divisors of 10 which occur in the sequence of d(k)'s, 1 <= k <= 10, are 1 and 2. So a(10) = 2.
From Michael De Vlieger, Oct 10 2017: (Start)
Records and their indices in a(n).
i = index in table
n = index of record r in this sequence
k = index of n in A002182.
MN(n) = rev(A054841(n)) = concatenation of multiplicities of
prime divisors of n, e.g., MN(60) = "211".
r = record in this sequence.
.
i n k MN(n) r
----------------------------
1 1 1 0 1
2 2 2 1 2
3 6 4 11 3
4 12 5 21 5
5 24 6 31 6
6 60 9 211 8
7 120 10 311 9
8 180 11 221 11
9 240 12 411 12
10 360 13 321 14
11 720 14 421 16
12 1260 16 2211 18
13 1680 17 4111 19
14 2520 18 3211 21
15 3360 5111 22
16 5040 19 4211 26
17 7560 20 3311 28
18 10080 21 5211 30
19 15120 22 4311 33
20 20160 23 6211 34
21 25200 24 4221 35
22 30240 5311 38
23 50400 27 5221 40
24 60480 6311 42
25 75600 4321 43
(End)
MATHEMATICA
f[n_] :=Length@ Select[Divisors[n], MemberQ[Table[Length@ Divisors[k], {k, n}], # ] &]; Table[f[n], {n, 105}] (* Ray Chandler, Dec 20 2006 *)
Block[{nn = 105, s}, s = DivisorSigma[0, Range@ nn]; Table[DivisorSum[n, 1 &, MemberQ[Take[s, n], #] &], {n, nn}]] (* Michael De Vlieger, Oct 10 2017 *)
PROG
(PARI) a(n) = #setintersect(divisors(n), Set(vector(n, k, numdiv(k)))); \\ Michel Marcus, Oct 11 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 18 2006
EXTENSIONS
Extended by Ray Chandler, Dec 20 2006
STATUS
approved