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A319354 a(n) = Product prime(k), where k ranges over the lengths of all arithmetic progressions formed from the divisors of n (with at least two distinct terms each); a(1) = 2 by convention.

%I A319354 #8 Sep 23 2018 20:59:46
%S A319354 2,3,3,27,3,1215,3,729,27,729,3,93002175,3,729,1215,59049,3,39858075,
%T A319354 3,14348907,729,729,3,576626970315375,27,729,729,23914845,3,
%U A319354 176518460300625,3,14348907,729,729,729,6305415920398625625,3,729,729,38127987424935,3,63546645708225,3,14348907,66430125,729,3,289588836976147679079375,27,14348907,729
%N A319354 a(n) = Product prime(k), where k ranges over the lengths of all arithmetic progressions formed from the divisors of n (with at least two distinct terms each); a(1) = 2 by convention.
%H A319354 Antti Karttunen, <a href="/A319354/b319354.txt">Table of n, a(n) for n = 1..4096</a>
%F A319354 For all n >= 1:
%F A319354 A061395(a(n)) = A067131(n).
%F A319354 A071178(a(n)) = A160752(n).
%F A319354 For all n >= 2, A001222(a(n)) = A066446(n).
%e A319354 For n = 6, the arithmetic progressions found in its divisor set {1, 2, 3, 6} are: {1, 2}, {1, 3}, {2, 3}, {2, 6}, {3, 6} and {1, 2, 3}. Five of these have length 2, and one is of length 3, thus a(6) = prime(2)^5 * prime(3) = 243*5 = 1215.
%o A319354 (PARI) A319354(n) = if(1==n,2,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 *= prime(c))); (m));
%Y A319354 Cf. A319355 (rgs-transform).
%K A319354 nonn
%O A319354 1,1
%A A319354 _Antti Karttunen_, Sep 21 2018