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A160752 a(n) is the number of sets of (distinct, not necessarily consecutive) positive divisors of n where each set has all of its elements in arithmetic progression, and where each set contains exactly A067131(n) elements.

%I A160752 #14 Sep 23 2018 20:58:41
%S A160752 1,1,1,3,1,1,1,6,3,6,1,1,1,6,1,10,1,2,1,15,6,6,1,2,3,6,6,1,1,4,1,15,6,
%T A160752 6,6,2,1,6,6,1,1,2,1,15,3,6,1,3,3,15,6,15,1,3,6,2,6,6,1,1,1,6,15,21,6,
%U A160752 3,1,15,6,28,1,4,1,6,2,15,6,2,1,2,10,6,1,2,6,6,6,28,1,10,1,15,6,6,6,4,1,15
%N A160752 a(n) is the number of sets of (distinct, not necessarily consecutive) positive divisors of n where each set has all of its elements in arithmetic progression, and where each set contains exactly A067131(n) elements.
%C A160752 If A067131(n) = 2, then a(n) = d(n)*(d(n)-1)/2, where d(n) is the number of divisors of n.
%C A160752 a(p) = 1 for all primes p.
%H A160752 Antti Karttunen, <a href="/A160752/b160752.txt">Table of n, a(n) for n = 1..65537</a>
%F A160752 a(n) = A071178(A319354(n)). - _Antti Karttunen_, Sep 21 2018
%e A160752 The divisors of 18 are 1,2,3,6,9,18. There are 2 sets of these divisors, (1,2,3) and (3,6,9), that have their terms in arithmetic progression and that each have the maximal number (3) of such divisors of 18. So a(18) = 2.
%o A160752 (PARI) A160752(n) = if(1==n,n,my(d=divisors(n),m=1,counts=vector(#d)); 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++); counts[c]++; m = max(m,c))); (counts[m])); \\ _Antti Karttunen_, Sep 21 2018
%Y A160752 Cf. A067131, A319354.
%K A160752 nonn
%O A160752 1,4
%A A160752 _Leroy Quet_, May 25 2009
%E A160752 Extended by _Ray Chandler_, Jun 15 2009