

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
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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



