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A294897 a(n) = Product_{d|n, gcd(d,n/d)>1} prime(A101296(gcd(d,n/d))-1).

%I A294897 #9 Nov 21 2017 21:36:10
%S A294897 1,1,1,2,1,1,1,4,2,1,1,4,1,1,1,12,1,4,1,4,1,1,1,16,2,1,4,4,1,1,1,36,1,
%T A294897 1,1,80,1,1,1,16,1,1,1,4,4,1,1,144,2,4,1,4,1,16,1,16,1,1,1,16,1,1,4,
%U A294897 252,1,1,1,4,1,1,1,1600,1,1,4,4,1,1,1,144,12,1,1,16,1,1,1,16,1,16,1,4,1,1,1,1296,1,4,4,80,1,1,1,16,1
%N A294897 a(n) = Product_{d|n, gcd(d,n/d)>1} prime(A101296(gcd(d,n/d))-1).
%H A294897 Antti Karttunen, <a href="/A294897/b294897.txt">Table of n, a(n) for n = 1..16384</a>
%H A294897 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A294897 a(n) = Product_{d|n} A008578(A101296(gcd(d,n/d))).
%F A294897 For n >= 1, A001222(a(n)) = A048105(n).
%o A294897 (PARI)
%o A294897 up_to = 16384
%o A294897 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A294897 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from _Charles R Greathouse IV_, Aug 17 2011
%o A294897 v101296 = rgs_transform(vector(up_to, n, A046523(n)));
%o A294897 A101296(n) = v101296[n];
%o A294897 A294897(n) = { my(m=1); fordiv(n,d,if(gcd(d,n/d)>1, m *= prime(A101296(gcd(d,n/d))-1))); m; };
%Y A294897 Cf. A005117 (the positions of ones).
%Y A294897 Cf. A101296, A294895.
%Y A294897 Cf. also A292258 (A292259), A293515, A294875 for similar filter sequences.
%K A294897 nonn
%O A294897 1,4
%A A294897 _Antti Karttunen_, Nov 21 2017