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

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

Cf. A032765-A032798.

Programs

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 *)

PARI

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

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)

Extensions

Typo in definition corrected by Zak Seidov, Aug 06 2016