A066427 Numbers with mu = 0 and infinitary MoebiusMu = -1; (sum of binary digits of prime exponents is odd).

4, 9, 16, 24, 25, 40, 49, 54, 56, 60, 72, 81, 84, 88, 90, 96, 104, 108, 121, 126, 128, 132, 135, 136, 140, 150, 152, 156, 160, 169, 180, 184, 189, 192, 198, 200, 204, 220, 224, 228, 232, 234, 240, 248, 250, 252, 256, 260, 276, 288, 289, 294, 296, 297, 300, 306

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

54 is in this sequence because its prime decomposition is 2^1 * 3^3, it is not squarefree and the binary digits of "1" and "3" add up to 3, an odd number.

Mathematica

iMoebiusMu[ n_ ] := Switch[ MoebiusMu[ n ], 1, 1, -1, -1, 0, If[ OddQ[ Plus@@(DigitCount[ Last[ Transpose[ FactorInteger[ n ] ] ], 2, 1 ]) ], -1, 1 ] ]; Select[ Range[ 400 ], MoebiusMu[ # ]===0 && iMoebiusMu[ # ]===-1 & ]

Prog

(PARI) is(n)=my(f=factor(n)[, 2]); #f && vecmax(f)>1 && vecsum(apply(hammingweight, f))%2 \\ Charles R Greathouse IV, Oct 15 2015

Crossrefs

Cf. A008683, A064179, A066428.

Sequence in context: A139588 A320894 A122986 * A320891 A161697 A078593

Adjacent sequences: A066424 A066425 A066426 * A066428 A066429 A066430

Keyword

easy,nonn

Author

Wouter Meeussen, Dec 27 2001

Status

approved