A306549 a(n) is the product of the positions of the zeros in the binary expansion of n (the most significant bit having position 1).

1, 1, 2, 1, 6, 2, 3, 1, 24, 6, 8, 2, 12, 3, 4, 1, 120, 24, 30, 6, 40, 8, 10, 2, 60, 12, 15, 3, 20, 4, 5, 1, 720, 120, 144, 24, 180, 30, 36, 6, 240, 40, 48, 8, 60, 10, 12, 2, 360, 60, 72, 12, 90, 15, 18, 3, 120, 20, 24, 4, 30, 5, 6, 1, 5040, 720, 840, 120, 1008

Offset

0,3

Comments

Apparently, the variant where the least significant bit has position 1 corresponds to A124773.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..16384

Formula

a(n) = A070939(n)! / A306286(n).

a(2*n) = a(n) * (1+A070939(n)).

a(2*n+1) = a(n).

a(2^k) = (k+1)! for any k >= 0.

a(2^k-1) = 1 for any k >= 0.

a(2^k-2) = k for any k >= 1.

Example

The first terms, alongside the positions of zeros and the binary representation of n, are:
  n   a(n)  Pos.zeros  bin(n)
  --  ----  ---------  ------
   0     1  {1}             0
   1     1  {}              1
   2     2  {2}            10
   3     1  {}             11
   4     6  {2,3}         100
   5     2  {2}           101
   6     3  {3}           110
   7     1  {}            111
   8    24  {2,3,4}      1000
   9     6  {2,3}        1001
  10     8  {2,4}        1010
  11     2  {2}          1011
  12    12  {3,4}        1100
  13     3  {3}          1101
  14     4  {4}          1110
  15     1  {}           1111

Prog

(PARI) a(n) = my (b=binary(n)); prod(k=1, #b, if (b[k]==0, k, 1))

Crossrefs

Cf. A070939, A124773, A306286.

Sequence in context: A325815 A292441 A333726 * A198870 A359273 A365048

Adjacent sequences: A306546 A306547 A306548 * A306550 A306551 A306552

Keyword

nonn,base,easy

Author

Rémy Sigrist, May 04 2019

Status

approved