A066427 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

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, A378489.

Sequence in context: A139588 A320894 A122986 * A378489 A320891 A161697

Adjacent sequences: A066424 A066425 A066426 * A066428 A066429 A066430

KEYWORD

easy,nonn,changed

AUTHOR

Wouter Meeussen, Dec 27 2001

STATUS

approved