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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

Table of n, a(n) for n=1..49.

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

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.)