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A032797 Numbers n such that n(n+1)(n+2)...(n+10) /(n+(n+1)+(n+2)+...+(n+10)) is a multiple of n. 0
1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 23, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 37, 38, 40, 41, 42, 43, 45, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 60, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 78, 79, 80, 81, 82, 84, 85, 86 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Equals natural numbers minus '6,11,17,22,28,...' (= previous term +5,+6,+5,+6,...).

LINKS

Table of n, a(n) for n=1..71.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 1, -1).

FORMULA

From Chai Wah Wu, Dec 17 2016: (Start)

a(n) = a(n-1) + a(n-9) - a(n-10) for n > 10.

G.f.: x*(x^9 + x^8 + x^7 + x^6 + 2*x^5 + x^4 + x^3 + x^2 + x + 1)/(x^10 - x^9 - x + 1). (End)

MATHEMATICA

nmnQ[n_]:=With[{c=n+Range[0, 10]}, Divisible[Times@@c/Total[c], n]]; Select[ Range[ 100], nmnQ] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 2, 3, 4, 5, 7, 8, 9, 10, 12}, 80] (* Harvey P. Dale, May 07 2017 *)

PROG

(PARI) is(n)=factorback(vector(10, i, n+i))%(11*n+55)==0 \\ Charles R Greathouse IV, Aug 07 2016

CROSSREFS

Cf. A032765-A032798.

Sequence in context: A039264 A231004 A039161 * A001967 A226066 A005838

Adjacent sequences:  A032794 A032795 A032796 * A032798 A032799 A032800

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest, May 15 1998

EXTENSIONS

Typo in definition corrected by Zak Seidov, Aug 06 2016

STATUS

approved

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Last modified February 20 20:55 EST 2019. Contains 320345 sequences. (Running on oeis4.)