A262481 Numbers m having in binary representation exactly lpf(m) ones, where lpf = least prime factor = A020639; a(1) = 1.

1, 6, 10, 12, 18, 20, 21, 24, 34, 36, 40, 48, 55, 66, 68, 69, 72, 80, 81, 96, 115, 130, 132, 136, 144, 155, 160, 185, 192, 205, 258, 260, 261, 264, 272, 273, 288, 295, 320, 321, 355, 384, 395, 425, 514, 516, 520, 528, 535, 544, 565, 576, 595, 623, 625, 637

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

A000120(a(n)) = A020639(a(n)).

Example

.   n | a(n) | A007088(a(n)) | factorization
. ----+------+---------------+--------------
.   1 |    1 |            1  |   1
.   2 |    6 |          110  |   2 * 3
.   3 |   10 |         1010  |   2 * 5
.   4 |   12 |         1100  |   2^2 * 3
.   5 |   18 |        10010  |   2 * 3^2
.   6 |   20 |        10100  |   2^2 * 5
.   7 |   21 |        10101  |   3 * 7
.   8 |   24 |        11000  |   2^3 * 3
.   9 |   34 |       100010  |   2 * 17
.  10 |   36 |       100100  |   2^2 * 3^2
.  11 |   40 |       101000  |   2^3 * 5
.  12 |   48 |       110000  |   2^4 * 3
.  13 |   55 |       110111  |   5 * 11
.  14 |   66 |      1000010  |   2 * 3 * 11
.  15 |   68 |      1000100  |   2^2 * 17
.  16 |   69 |      1000101  |   3 * 23
.  17 |   72 |      1001000  |   2^3 * 3^2
.  18 |   80 |      1010000  |   2^4 * 5
.  19 |   81 |      1010001  |   3^4
.  20 |   96 |      1100000  |   2^5 * 3
.  21 |  115 |      1110011  |   5 * 23
.  22 |  130 |     10000010  |   2 * 5 * 13
.  23 |  132 |     10000100  |   2^2 * 3 * 11
.  24 |  136 |     10001000  |   2^3 * 17
.  25 |  144 |     10010000  |   2^4 * 3^2  .

Mathematica

Select[Range[640], FactorInteger[#][[1, 1]] == DigitCount[#, 2, 1] &] (* Amiram Eldar, Jul 24 2023 *)

Prog

(Haskell)
a262481 n = a262481_list !! (n-1)
a262481_list = filter (\x -> a000120 x == a020639 x) [1..]
(PARI) isok(n) = (n==1) || (hammingweight(n) == factor(n)[1, 1]); \\ Michel Marcus, Sep 29 2015

Crossrefs

Cf. A000120, A020639, A007088.

Subsequence of A052294.

Sequence in context: A315125 A316991 A316992 * A119689 A351614 A066038

Adjacent sequences: A262478 A262479 A262480 * A262482 A262483 A262484

Keyword

nonn,base

Author

Reinhard Zumkeller, Sep 24 2015

Status

approved