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A071594
Numbers k such that the number of 1's in the binary representation of k equals omega(k), the number of distinct primes in the factorization of k.
5
2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 32, 33, 34, 36, 40, 42, 48, 64, 65, 68, 70, 72, 80, 84, 96, 128, 129, 136, 138, 140, 144, 160, 168, 192, 210, 256, 266, 272, 273, 276, 280, 288, 290, 320, 322, 330, 336, 384, 385, 390, 420, 512, 513, 514, 518, 522, 530, 532
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2000 from Ivan Neretin)
EXAMPLE
129 = 10000001 in base 2 and 129 = 3*43 hence 129 is in the sequence.
MATHEMATICA
Select[Range[2, 1000], Length[FactorInteger[#]] == DigitCount[#, 2, 1] &] (* Ivan Neretin, May 30 2015 *)
PROG
(PARI) for(n=1, 1000, if(sum(i=1, length(binary(n)), component(binary(n), i))==omega(n), print1(n, ", ")))
(PARI) select(n->hammingweight(n)==omega(n), vector(1000, n, n)) \\ Michel Marcus, May 30 2015
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Benoit Cloitre, Jun 01 2002
EXTENSIONS
Name edited by Amiram Eldar, Jan 11 2020
STATUS
approved