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A132748
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a(n) = the sum of the positive non-isolated divisors of n.
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3
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0, 3, 0, 3, 0, 6, 0, 3, 0, 3, 0, 10, 0, 3, 0, 3, 0, 6, 0, 12, 0, 3, 0, 10, 0, 3, 0, 3, 0, 17, 0, 3, 0, 3, 0, 10, 0, 3, 0, 12, 0, 19, 0, 3, 0, 3, 0, 10, 0, 3, 0, 3, 0, 6, 0, 18, 0, 3, 0, 21, 0, 3, 0, 3, 0, 6, 0, 3, 0, 3, 0, 27, 0, 3, 0, 3, 0, 6, 0, 12, 0, 3, 0, 23, 0, 3, 0, 3, 0, 36, 0, 3, 0, 3, 0, 10, 0, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A divisor, d, of n is non-isolated if either (d-1) or (d+1) divides n.
a(2n-1) = 0 for all n >= 1.
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FORMULA
| a(n) = A000203(n) - A132882(n), where A000203 is sigma(n), sum of divisors of n.
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EXAMPLE
| The positive divisors of 20 are 1,2,4,5,10,20. Of these, 1 and 2 are next to each other and 4 and 5 are next to each other. So a(20) = 1+2+4+5 = 12.
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MATHEMATICA
| Table[Plus @@ (Select[Divisors[n], If[ # > 1, Mod[n, #*(# - 1)] == 0] || Mod[n, #*(# + 1)] == 0 &]), {n, 1, 80}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 01 2007
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CROSSREFS
| Cf. A129308, A132747.
Sequence in context: A194084 A100258 A045763 * A055945 A138123 A127372
Adjacent sequences: A132745 A132746 A132747 * A132749 A132750 A132751
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Aug 27 2007
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 01 2007
Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 24 2008
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