A066428 Numbers with mu = 0 and infinitary MoebiusMu = +1 (sum of binary digits of prime exponents is even).

8, 12, 18, 20, 27, 28, 32, 36, 44, 45, 48, 50, 52, 63, 64, 68, 75, 76, 80, 92, 98, 99, 100, 112, 116, 117, 120, 124, 125, 144, 147, 148, 153, 162, 164, 168, 171, 172, 175, 176, 188, 196, 207, 208, 212, 216, 225, 236, 242, 243, 244, 245, 261, 264, 268, 270, 272

Offset

1,1

Links

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

Example

28 is in this sequence because its prime decomposition is 2^2* 7^1, it is not squarefree and the binary digits of "2" and "1" add up to 2, an even 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==0 \\ Charles R Greathouse IV, Oct 15 2015

Crossrefs

Cf. A064179, A066427.

Sequence in context: A226527 A212582 A046369 * A228056 A187042 A370650

Adjacent sequences: A066425 A066426 A066427 * A066429 A066430 A066431

Keyword

easy,nonn

Author

Wouter Meeussen, Dec 27 2001

Status

approved