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A162952
A positive integer n is included if n and the number of divisors of n contain the same number of 1's in their binary representations.
4
1, 2, 8, 9, 12, 18, 20, 36, 48, 68, 72, 80, 96, 128, 132, 160, 260, 272, 288, 448, 516, 528, 544, 704, 720, 768, 832, 900, 1025, 1028, 1040, 1056, 1152, 1200, 1216, 1280, 1296, 1344, 1536, 1584, 1600, 2050, 2052, 2064, 2080, 2240, 2352, 2368, 2448, 2560, 2624
OFFSET
1,2
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 638 terms from Michael De Vlieger)
EXAMPLE
20 has 6 divisors. 20 in binary is 10100, while 6 in binary is 110. Since both 10100 and 110 contain the same number of 1's (two 1's each), then 20 is in the sequence.
MAPLE
read("transforms") ; isA162952 := proc(n) RETURN( wt(n) = wt(numtheory[tau](n)) ) ; end: for n from 1 to 10000 do if isA162952(n) then printf("%d, ", n) ; fi; od: # R. J. Mathar, Jul 30 2009
MATHEMATICA
Select[Range[2^12], SameQ @@ DigitCount[{#, DivisorSigma[0, #]}, 2, 1] &] (* Michael De Vlieger, Nov 04 2017 *)
PROG
(PARI) isok(n) = (hammingweight(n) == hammingweight(numdiv(n))); \\ Michel Marcus, Nov 04 2017
CROSSREFS
Cf. A162953.
Sequence in context: A289146 A294374 A066550 * A033950 A046526 A279373
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Jul 18 2009
EXTENSIONS
Extended beyond a(10) by R. J. Mathar, Jul 30 2009
STATUS
approved