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A332306 a(n) is the least k such that A121663(k) = n. 1
0, 1, 2, 4, 8, 3, 32, 5, 128, 9, 512, 6, 2048, 33, 10, 65, 32768, 18, 131072, 12, 34, 513, 2097152, 7, 8388608, 2049, 130, 36, 134217728, 11, 536870912, 68, 514, 32769, 40, 19, 34359738368, 131073, 2050, 13, 549755813888, 35, 2199023255552, 516, 136, 2097153 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The binary representation of a(n) encodes the colexicographically earliest factorization of n into distinct factors greater than 1.

LINKS

Table of n, a(n) for n=1..46.

Rémy Sigrist, PARI program for A332306

FORMULA

a(n) = 2^(n-2) iff n is a prime number of the square of a prime number (A000430).

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

a(p_1*...*p_k) = 2^(p_1-2)+...+2^(p_k-2) for distinct primes numbers p_1, ..., p_k.

EXAMPLE

The first terms, alongside their binary representations and factorizations, are:

  n   a(n)    bin(a(n))           Factorization

  --  ------  ------------------  -------------

   1       0                   0

   2       1                   1              2

   3       2                  10              3

   4       4                 100              4

   5       8                1000              5

   6       3                  11            2*3

   7      32              100000              7

   8       5                 101            2*4

   9     128            10000000              9

  10       9                1001            2*5

  11     512          1000000000             11

  12       6                 110            3*4

  13    2048        100000000000             13

  14      33              100001            2*7

  15      10                1010            3*5

  16      65             1000001            2*8

  17   32768    1000000000000000             17

  18      18               10010            3*6

  19  131072  100000000000000000             19

  20      12                1100            4*5

PROG

(PARI) See Links section.

CROSSREFS

Cf. A000430, A045778, A121663.

Sequence in context: A243065 A289271 A341811 * A223699 A231610 A225124

Adjacent sequences:  A332303 A332304 A332305 * A332307 A332308 A332309

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Feb 09 2020

STATUS

approved

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Last modified April 23 06:38 EDT 2021. Contains 343201 sequences. (Running on oeis4.)