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A071562
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Numbers n such that the sum of the middle divisors of n (A071090) are not zero.
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6
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1, 2, 4, 6, 8, 9, 12, 15, 16, 18, 20, 24, 25, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 50, 54, 56, 60, 63, 64, 66, 70, 72, 77, 80, 81, 84, 88, 90, 91, 96, 98, 99, 100, 104, 108, 110, 112, 117, 120, 121, 126, 128, 130, 132, 135, 140, 143, 144, 150, 153, 154, 156, 160
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Numbers occurring in A100345 (except 0). [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 04 2010]
This sequence is closed under multiplication. If n = a*b with a <= b <= 2a, and m = c*d with c <= d <= 2c, then min(a*d,b*c)*max(a*d,b*c) is a factorization of m*n with the specified property. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 07 2010]
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FORMULA
| Numbers of form m*k with m <= k <= 2m. - Vladeta Jovovic (vladeta(AT)eunet.rs), May 07 2005
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MATHEMATICA
| f[n_] := Plus @@ Select[ Divisors[n], Sqrt[n/2] <= # < Sqrt[n*2] &]; Select[ Range[175], f[ # ] != 0 &]
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CROSSREFS
| Cf. A071090, A071561.
Also n such that A067742(n) is nonzero.
Cf. A067742, A100345, A175040. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 04 2010]
Cf. A176039 (primitive elements). [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 07 2010]
Sequence in context: A189170 A138969 A161819 * A100345 A118363 A146982
Adjacent sequences: A071559 A071560 A071561 * A071563 A071564 A071565
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), May 30 2002
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