A124656 Abundant odious numbers. (Abundant numbers that have an odd number of ones in their binary representation.)

42, 56, 70, 84, 88, 100, 104, 112, 138, 140, 162, 168, 174, 176, 186, 196, 200, 208, 220, 224, 234, 276, 280, 304, 324, 336, 342, 348, 352, 364, 372, 392, 400, 416, 426, 440, 448, 460, 468, 522, 532, 546, 552, 558, 560, 570, 572, 580, 608, 618, 620, 642, 644

Offset

1,1

Links

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

Example

56 is in the sequence because the sum of its divisors, 1 + 2 + 4 + 7 + 8 + 14 + 28 + 56 = 120 > 2*56 and its base-2 representation (111000) has an odd number of 1's.

Maple

with(numtheory): a:=proc(n) local n2: n2:=convert(n, base, 2): if add(n2[j], j=1..nops(n2)) mod 2 = 1 and sigma(n)>2*n then n else fi end: seq(a(n), n=1..750); # Emeric Deutsch, Jan 01 2007

Mathematica

Select[Range[650], OddQ @ DigitCount[#, 2][[1]] && DivisorSigma[1, #] > 2# &] (* Amiram Eldar, Dec 09 2019 *)

Crossrefs

Intersection of A005101 (abundant numbers) and A000069 (odious numbers).

Sequence in context: A043136 A039313 A043916 * A002706 A080971 A039384

Adjacent sequences: A124653 A124654 A124655 * A124657 A124658 A124659

Keyword

base,nonn

Author

Tanya Khovanova, Dec 27 2006

Extensions

More terms from Emeric Deutsch, Jan 01 2007

Status

approved