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A082662 Numbers k such that A001227(k) = A082647(k). 4
1, 2, 4, 6, 8, 12, 16, 20, 24, 28, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304, 320, 336, 352, 368, 384, 400, 416, 432, 448, 464, 480, 496, 512, 544, 576, 608, 640, 672, 704, 736, 768, 800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

That is, numbers such that A000265(n) <= A000203(A006519(n)) or also such that A000265(n) <= A038712(n). - Michel Marcus, Aug 14 2014

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

LINKS

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

Eric Weisstein's World of Mathematics, Even Part

Eric Weisstein's World of Mathematics, Odd Part

FORMULA

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).

MATHEMATICA

cnt[n_] := DivisorSum[n, Boole[OddQ[#] && #>Sqrt[2n]]&]; Select[Range[800], cnt[#]==0&] (* Jean-Fran├žois Alcover, Feb 16 2017 *)

PROG

(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

CROSSREFS

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

Sequence in context: A279686 A219653 A050622 * A246663 A182568 A064522

Adjacent sequences:  A082659 A082660 A082661 * A082663 A082664 A082665

KEYWORD

easy,nonn

AUTHOR

Naohiro Nomoto, May 18 2003

STATUS

approved

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Last modified September 18 12:00 EDT 2019. Contains 327170 sequences. (Running on oeis4.)