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

Author

Wouter Meeussen, Dec 27 2001

Keywords

• easy
• nonn

Comments

First differs from A378489 (the intersection of A000028 and A028260) by the inclusion of 72. - Peter Munn, Jul 13 2024

Examples

			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.
		

Links

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

Crossrefs

Cf. A008683, A064179, A066428, A378489.

Programs

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 & ]

PARI

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