cp's OEIS Frontend

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

%I A067131 #13 Sep 23 2018 20:56:46
%S A067131 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,
%T A067131 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,
%U A067131 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
%N A067131 Number of elements in the largest set of divisors of n which are in arithmetic progression.
%H A067131 Antti Karttunen, <a href="/A067131/b067131.txt">Table of n, a(n) for n = 1..65537</a>
%F A067131 a(n) = A061395(A319354(n)). - _Antti Karttunen_, Sep 21 2018
%e A067131 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}.
%t A067131 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]
%o A067131 (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
%Y A067131 Cf. A067132, A091009, A160752, A319354.
%K A067131 easy,nonn
%O A067131 1,2
%A A067131 _Amarnath Murthy_, Jan 09 2002
%E A067131 Edited by _Dean Hickerson_, Jan 15 2002