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A126131 a(n) = number of divisors of n which equal any d(k) for 1 <= k <= n, where d(k) is the number of positive divisors of k. 4
1, 2, 1, 2, 1, 3, 1, 3, 2, 2, 1, 5, 1, 2, 2, 3, 1, 4, 1, 4, 2, 2, 1, 6, 2, 2, 2, 3, 1, 5, 1, 4, 2, 2, 2, 6, 1, 2, 2, 5, 1, 4, 1, 3, 4, 2, 1, 6, 1, 4, 2, 3, 1, 5, 2, 4, 2, 2, 1, 8, 1, 2, 3, 4, 2, 4, 1, 3, 2, 5, 1, 8, 1, 2, 3, 3, 2, 4, 1, 6, 3, 2, 1, 7, 2, 2, 2, 4, 1, 7, 2, 3, 2, 2, 2, 7, 1, 3, 3, 5, 1, 4, 1, 4, 4 (list; graph; refs; listen; history; text; internal format)
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

Cf. A126132.

Sequence in context: A029238 A208478 A274450 * A138012 A072531 A025818

Adjacent sequences:  A126128 A126129 A126130 * A126132 A126133 A126134

KEYWORD

nonn

AUTHOR

Leroy Quet, Dec 18 2006

EXTENSIONS

Extended by Ray Chandler, Dec 20 2006

STATUS

approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)