A378489 -id:A378489 - cp's OEIS frontend

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

Wouter Meeussen, Dec 27 2001

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

			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.

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

Cf. A008683, A064179, A066428, A378489.

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 & ]

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

A378494 Intersection of A000379 and A026424.

Original entry on oeis.org

8, 12, 18, 20, 27, 28, 32, 44, 45, 48, 50, 52, 63, 68, 75, 76, 80, 92, 98, 99, 112, 116, 117, 120, 124, 125, 147, 148, 153, 162, 164, 168, 171, 172, 175, 176, 188, 207, 208, 212, 236, 242, 243, 244, 245, 261, 264, 268, 270, 272, 275, 279, 280, 284, 292, 304, 312, 316

Offset: 1

Paolo Xausa, Nov 28 2024, following a suggestion from Peter Munn

nonn

First differs from A187042 at n = 24, where a(24) = 120 is missing from A187042.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A000379, A026424, A187042, A378489.

A000379Q[k_] := k == 1 || EvenQ[Count[IntegerDigits[FactorInteger[k][[All, 2]], 2], 1, 2]];
A026424Q[k_] := OddQ[PrimeOmega[k]];
Select[Range[500], A000379Q[#] && A026424Q[#] &]

cp's OEIS Frontend

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

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