A032797 Numbers n such that n(n+1)(n+2)...(n+10) /(n+(n+1)+(n+2)+...+(n+10)) is a multiple of n.

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

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