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 A082662 Numbers k such that A001227(k) = A082647(k). 4

%I

%S 1,2,4,6,8,12,16,20,24,28,32,40,48,56,64,72,80,88,96,104,112,120,128,

%T 144,160,176,192,208,224,240,256,272,288,304,320,336,352,368,384,400,

%U 416,432,448,464,480,496,512,544,576,608,640,672,704,736,768,800

%N Numbers k such that A001227(k) = A082647(k).

%C Numbers n such that the odd part of n is less than or equal to the sum of divisors of the even part, with equality if and only if n is an even perfect number. A subsequence of A005153. - _Jaycob Coleman_, Jun 21 2014

%C That is, numbers such that A000265(n) <= A000203(A006519(n)) or also such that A000265(n) <= A038712(n). - _Michel Marcus_, Aug 14 2014

%C Conjecture: numbers n such that there are no pairs of equidistant subparts in the symmetric representation of sigma(n). The complement of this sequence is A281005. - _Omar E. Pol_, Apr 18 2017

%H Amiram Eldar, <a href="/A082662/b082662.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EvenPart.html">Even Part</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OddPart.html">Odd Part</a>

%F a(1) = 1. a(3*2^m + k - 2) = 2^(2m+1) + (k-1)*2^(m+1), where m >= 0, k=1..(3*2^m).

%t cnt[n_] := DivisorSum[n, Boole[OddQ[#] && #>Sqrt[2n]]&]; Select[Range[800], cnt[#]==0&] (* _Jean-François Alcover_, Feb 16 2017 *)

%o (PARI) isok(n) = my(q = sqrt(2*n)); (sumdiv(n, d, (d%2) && (d < q)) == sumdiv(n, d, d%2)); \\ _Michel Marcus_, Jul 04 2014

%Y Cf. A000203, A000265, A001227, A006519, A038712, A082647, A237593, A279387, A281005 (complement).

%K easy,nonn

%O 1,2

%A _Naohiro Nomoto_, May 18 2003

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Last modified October 23 13:38 EDT 2019. Contains 328345 sequences. (Running on oeis4.)