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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A000120(a(n)) = A056169(a(n)). LINKS 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) 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[#], #[]==1&]] == DigitCount[ #, 2, 1]&] (* Harvey P. Dale, Apr 30 2014 *) CROSSREFS Cf. A000120, A056169. Sequence in context: A283909 A107385 A321727 * A233896 A118039 A218965 Adjacent sequences:  A145538 A145539 A145540 * A145542 A145543 A145544 KEYWORD nonn AUTHOR Leroy Quet, Oct 12 2008 EXTENSIONS Extended by R. J. Mathar, Oct 16 2008 STATUS approved

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Last modified October 16 02:52 EDT 2019. Contains 328038 sequences. (Running on oeis4.)