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A145541
A positive integer n is included if (the number of 1's in the binary representation of n) = (the number of exponents equal to 1 in the prime factorization of n).
0
2, 6, 10, 33, 34, 42, 65, 70, 129, 132, 138, 210, 260, 264, 266, 273, 290, 322, 330, 385, 390, 514, 516, 518, 520, 528, 530, 642, 1026, 1030, 1032, 1034, 1040, 1056, 1090, 1092, 1122, 1155, 1218, 1281, 1290, 1410, 1540, 1554, 1794, 2049, 2050, 2054, 2064
OFFSET
1,1
COMMENTS
A000120(a(n)) = A056169(a(n)).
EXAMPLE
132 has the prime factorization 2^2 * 3^1 * 11^1. This has 2 exponents each equal to 1. 132 in binary is 10000100, which has two 1's. Since the number of exponents in the prime factorization equals the number of 1's in the binary representation, then 132 is included in the sequence.
MAPLE
A000120 := proc(n) add(i, i=convert(n, base, 2)) ; end: A056169 := proc(n) a :=0 ; for p in ifactors(n)[2] do if op(2, p) = 1 then a := a+1 ; fi; od: RETURN(a) ; end: isA145541 := proc(n) RETURN( A000120(n) = A056169(n)) ; end: for n from 1 to 3000 do if isA145541(n) then printf("%d, ", n) ; fi; od: # R. J. Mathar, Oct 16 2008
MATHEMATICA
Select[Range[2, 2100], Length[Select[FactorInteger[#], #[[2]]==1&]] == DigitCount[ #, 2, 1]&] (* Harvey P. Dale, Apr 30 2014 *)
CROSSREFS
Sequence in context: A332321 A283846 A321727 * A233896 A118039 A218965
KEYWORD
nonn
AUTHOR
Leroy Quet, Oct 12 2008
EXTENSIONS
Extended by R. J. Mathar, Oct 16 2008
STATUS
approved