cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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