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 A138652 Number of differences (not all necessarily distinct) between consecutive divisors of 2n which are also divisors of 2n. 2
 1, 2, 3, 3, 2, 5, 2, 4, 5, 5, 2, 7, 2, 4, 6, 5, 2, 8, 2, 6, 7, 4, 2, 9, 3, 4, 7, 5, 2, 11, 2, 6, 6, 4, 3, 11, 2, 4, 6, 7, 2, 10, 2, 6, 10, 4, 2, 11, 3, 8, 6, 6, 2, 11, 5, 6, 6, 4, 2, 15, 2, 4, 9, 7, 4, 9, 2, 6, 6, 8, 2, 14, 2, 4, 9, 6, 2, 11, 2, 8, 9, 4, 2, 15, 4, 4, 6, 6, 2, 17, 3, 6, 6, 4, 4, 13, 2, 6, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For n = any odd positive integer, there are no differences (between consecutive divisors of n) that divide n. LINKS Antti Karttunen, Table of n, a(n) for n = 1..20000 FORMULA a(n) + A360118(2n) = A000005(2n)-1, i.e., a(n) = A066660(n) - A360118(2*n). - Reference to a wrong A-number replaced with A360118 by Antti Karttunen, Feb 20 2023 EXAMPLE From Antti Karttunen, Feb 20 2023: (Start) Divisors of 2*12 = 24 are: [1, 2, 3, 4, 6, 8, 12, 24]. Their first differences are: [1, 1, 1, 2, 2, 4, 12], all 7 which are divisors of 24, thus a(12) = 7. Divisors of 2*35 = 70 are: [1, 2, 5, 7, 10, 14, 35, 70]. Their first differences are: 1, 3, 2, 3, 4, 21, 35, of which 1, 2 and 35 are divisors of 70, thus a(35) = 3. Divisors of 2*65 = 130 are: [1, 2, 5, 10, 13, 26, 65, 130]. Their first differences are: 1, 3, 5, 3, 13, 39, 65, of which 1, 5, 13 and 65 are divisors of 130, thus a(65) = 4. (End) MAPLE A138652 := proc(n) local a, dvs, i ; a := 0 ; dvs := sort(convert(numtheory[divisors](2*n), list)) ; for i from 2 to nops(dvs) do if (2*n) mod ( op(i, dvs)-op(i-1, dvs) ) = 0 then a := a+1 ; fi ; od: a ; end: seq(A138652(n), n=1..120) ; # R. J. Mathar, May 20 2008 MATHEMATICA a = {}; For[n = 2, n < 200, n = n + 2, b = Table[Divisors[n][[i + 1]] - Divisors[n][[i]], {i, 1, Length[Divisors[n]] - 1}]; AppendTo[a, Length[Select[b, Mod[n, # ] == 0 &]]]]; a (* Stefan Steinerberger, May 18 2008 *) PROG (PARI) A138652(n) = { n = 2*n; my(d=divisors(n), erot = vector(#d-1, k, d[k+1] - d[k])); sum(i=1, #erot, !(n%erot[i])); }; \\ Antti Karttunen, Feb 20 2023 CROSSREFS Cf. A060741, A060763, A066660, A360118. Sequence in context: A034799 A008985 A326699 * A323833 A131899 A095174 Adjacent sequences: A138649 A138650 A138651 * A138653 A138654 A138655 KEYWORD nonn AUTHOR Leroy Quet, May 15 2008 EXTENSIONS More terms from Stefan Steinerberger and R. J. Mathar, May 18 2008 Definition edited and clarified by Antti Karttunen, Feb 20 2023 STATUS approved

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Last modified May 29 05:33 EDT 2024. Contains 372921 sequences. (Running on oeis4.)