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 A132747 a(n) = number of non-isolated divisors of n. 11
 0, 2, 0, 2, 0, 3, 0, 2, 0, 2, 0, 4, 0, 2, 0, 2, 0, 3, 0, 4, 0, 2, 0, 4, 0, 2, 0, 2, 0, 5, 0, 2, 0, 2, 0, 4, 0, 2, 0, 4, 0, 5, 0, 2, 0, 2, 0, 4, 0, 2, 0, 2, 0, 3, 0, 4, 0, 2, 0, 6, 0, 2, 0, 2, 0, 3, 0, 2, 0, 2, 0, 6, 0, 2, 0, 2, 0, 3, 0, 4, 0, 2, 0, 6, 0, 2, 0, 2, 0, 7, 0, 2, 0, 2, 0, 4, 0, 2, 0, 4, 0, 3, 0, 2, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. LINKS Ray Chandler, Table of n, a(n) for n=1..10000 FORMULA a(n) = A000005(n) - A132881(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) = the number of these divisors, which is 4. MATHEMATICA Table[Length[Select[Divisors[n], If[ # > 1, IntegerQ[n/(#*(# - 1))]] || IntegerQ[n/(#*(# + 1))] &]], {n, 1, 90}] (* Stefan Steinerberger, Oct 26 2007 *) PROG (PARI) a(n) = my(div = divisors(n)); sumdiv(n, d, vecsearch(div, d-1) || vecsearch(div, d+1)); \\ Michel Marcus, Aug 22 2014 CROSSREFS Cf. A129308, A132748. Sequence in context: A324848 A090330 A332447 * A301979 A183063 A318979 Adjacent sequences:  A132744 A132745 A132746 * A132748 A132749 A132750 KEYWORD nonn AUTHOR Leroy Quet, Aug 27 2007 EXTENSIONS More terms from Stefan Steinerberger, Oct 26 2007 Extended by Ray Chandler, Jun 24 2008 STATUS approved

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Last modified April 10 02:39 EDT 2020. Contains 333392 sequences. (Running on oeis4.)