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A283478 a(n) = A097248(A108951(n)).

%I A283478 #12 May 15 2017 19:56:22
%S A283478 1,2,6,3,30,5,210,6,15,7,2310,10,30030,11,21,5,510510,30,9699690,14,
%T A283478 33,13,223092870,15,105,17,14,22,6469693230,42,200560490130,10,39,19,
%U A283478 165,7,7420738134810,23,51,21,304250263527210,66,13082761331670030,26,70,29,614889782588491410,30,1155,210,57,34,32589158477190044730,21,195,33,69,31
%N A283478 a(n) = A097248(A108951(n)).
%H A283478 Antti Karttunen, <a href="/A283478/b283478.txt">Table of n, a(n) for n = 1..1024</a>
%F A283478 a(n) = A097248(A108951(n)).
%F A283478 Other identities:
%F A283478 For all n >= 0, a(A019565(n)) = A283475(n).
%t A283478 Table[FixedPoint[Times @@ Map[#1^#2 & @@ # &, Partition[#, 2, 2] &@ Flatten[FactorInteger[#] /. {p_, e_} /; e >= 2 :> {If[OddQ@ e, {p, 1}, {1, 1}], {NextPrime@ p, Floor[e/2]}}]] &, #] &[Times @@ Map[#1^#2 & @@ # &, FactorInteger[n] /. {p_, e_} /; e > 0 :> {Times @@ Prime@ Range@ PrimePi@ p, e}]], {n, 58}] (* _Michael De Vlieger_, Mar 18 2017 *)
%o A283478 (PARI)
%o A283478 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A283478 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From _Charles R Greathouse IV_, Jun 28 2015
%o A283478 A097246(n) = { my(f=factor(n)); prod(i=1, #f~, (nextprime(f[i,1]+1)^(f[i,2]\2))*((f[i,1])^(f[i,2]%2))); };
%o A283478 A097248(n) = { my(k=A097246(n)); while(k<>n, n = k; k = A097246(k)); k; };
%o A283478 A283478(n) = A097248(A108951(n));
%o A283478 (Scheme) (define (A283478 n) (A097248 (A108951 n)))
%o A283478 (Python)
%o A283478 from sympy import primerange, factorint, nextprime
%o A283478 from operator import mul
%o A283478 def P(n): return reduce(mul, [i for i in primerange(2, n + 1)])
%o A283478 def a108951(n):
%o A283478     f = factorint(n)
%o A283478     return 1 if n==1 else reduce(mul, [P(i)**f[i] for i in f])
%o A283478 def a097246(n):
%o A283478     f=factorint(n)
%o A283478     return 1 if n==1 else reduce(mul, [(nextprime(i)**int(f[i]/2))*(i**(f[i]%2)) for i in f])
%o A283478 def a097248(n):
%o A283478     k=a097246(n)
%o A283478     while k!=n:
%o A283478         n=k
%o A283478         k=a097246(k)
%o A283478     return k
%o A283478 def a(n): return a097248(a108951(n)) # _Indranil Ghosh_, May 15 2017
%Y A283478 Cf. A019565, A097248, A108951, A283475.
%K A283478 nonn
%O A283478 1,2
%A A283478 _Antti Karttunen_, Mar 16 2017