This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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