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%I #16 Jul 24 2023 02:35:43
%S 1,6,10,12,18,20,21,24,34,36,40,48,55,66,68,69,72,80,81,96,115,130,
%T 132,136,144,155,160,185,192,205,258,260,261,264,272,273,288,295,320,
%U 321,355,384,395,425,514,516,520,528,535,544,565,576,595,623,625,637
%N Numbers m having in binary representation exactly lpf(m) ones, where lpf = least prime factor = A020639; a(1) = 1.
%H Reinhard Zumkeller, <a href="/A262481/b262481.txt">Table of n, a(n) for n = 1..10000</a>
%F A000120(a(n)) = A020639(a(n)).
%e . n | a(n) | A007088(a(n)) | factorization
%e . ----+------+---------------+--------------
%e . 1 | 1 | 1 | 1
%e . 2 | 6 | 110 | 2 * 3
%e . 3 | 10 | 1010 | 2 * 5
%e . 4 | 12 | 1100 | 2^2 * 3
%e . 5 | 18 | 10010 | 2 * 3^2
%e . 6 | 20 | 10100 | 2^2 * 5
%e . 7 | 21 | 10101 | 3 * 7
%e . 8 | 24 | 11000 | 2^3 * 3
%e . 9 | 34 | 100010 | 2 * 17
%e . 10 | 36 | 100100 | 2^2 * 3^2
%e . 11 | 40 | 101000 | 2^3 * 5
%e . 12 | 48 | 110000 | 2^4 * 3
%e . 13 | 55 | 110111 | 5 * 11
%e . 14 | 66 | 1000010 | 2 * 3 * 11
%e . 15 | 68 | 1000100 | 2^2 * 17
%e . 16 | 69 | 1000101 | 3 * 23
%e . 17 | 72 | 1001000 | 2^3 * 3^2
%e . 18 | 80 | 1010000 | 2^4 * 5
%e . 19 | 81 | 1010001 | 3^4
%e . 20 | 96 | 1100000 | 2^5 * 3
%e . 21 | 115 | 1110011 | 5 * 23
%e . 22 | 130 | 10000010 | 2 * 5 * 13
%e . 23 | 132 | 10000100 | 2^2 * 3 * 11
%e . 24 | 136 | 10001000 | 2^3 * 17
%e . 25 | 144 | 10010000 | 2^4 * 3^2 .
%t Select[Range[640], FactorInteger[#][[1, 1]] == DigitCount[#, 2, 1] &] (* _Amiram Eldar_, Jul 24 2023 *)
%o (Haskell)
%o a262481 n = a262481_list !! (n-1)
%o a262481_list = filter (\x -> a000120 x == a020639 x) [1..]
%o (PARI) isok(n) = (n==1) || (hammingweight(n) == factor(n)[1,1]); \\ _Michel Marcus_, Sep 29 2015
%Y Cf. A000120, A020639, A007088.
%Y Subsequence of A052294.
%K nonn,base
%O 1,2
%A _Reinhard Zumkeller_, Sep 24 2015
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