A067131 Number of elements in the largest set of divisors of n which are in arithmetic progression.

1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 6, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2, 4, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 3, 2

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = A061395(A319354(n)). - Antti Karttunen, Sep 21 2018

Example

a(12) = 4 as the divisors of 12 are {1,2,3,4,6,12} and the maximal subset in arithmetic progression is {1,2,3,4}. a(15) = 3; the maximal set is {1,3,5}.

Mathematica

lap[s_] := Module[{}, l=Length[s]; If[l<2, Return[l]]; val=2; For[i=1, i<l, i++, For[j=i+1, j<=l, j++, For[k=2, MemberQ[s, k*s[[j]]-(k-1)s[[i]]], k++, Null]; If[k>val, val=k]]]; val]; lap/@Divisors/@Range[1, 200]

Prog

(PARI) A067131(n) = { my(d=divisors(n), m=1); for(i=1, (#d-1), for(j=(i+1), #d, my(c=1, k=d[j], s=(d[j]-d[i])); while(!(n%k), k+=s; c++); m = max(m, c))); (m); }; \\ Antti Karttunen, Sep 21 2018

Crossrefs

Cf. A067132, A091009, A160752, A319354.

Sequence in context: A020649 A362366 A183024 * A094915 A217619 A187186

Adjacent sequences: A067128 A067129 A067130 * A067132 A067133 A067134

Keyword

easy,nonn

Author

Amarnath Murthy, Jan 09 2002

Extensions

Edited by Dean Hickerson, Jan 15 2002

Status

approved