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
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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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 & ]
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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