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Search: id:A132748
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A132748 a(n) = the sum of the positive non-isolated divisors of n. +0
4
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; listen)
OFFSET

1,2

COMMENT

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.

LINKS

Leroy Quet, Home Page (listed in lieu of email address)

FORMULA

a(n) = A000203(n) - A132882(n), where A000203 is sigma(n), sum of divisors of n.

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.

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

CROSSREFS

Cf. A129308, A132747.

Sequence in context: A141030 A100258 A045763 this_sequence A055945 A138123 A127372

Adjacent sequences: A132745 A132746 A132747 this_sequence A132749 A132750 A132751

KEYWORD

nonn

AUTHOR

Leroy Quet Aug 27 2007

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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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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