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a(n) = A097248(A108951(n)).
4

%I #12 May 15 2017 19:56:22

%S 1,2,6,3,30,5,210,6,15,7,2310,10,30030,11,21,5,510510,30,9699690,14,

%T 33,13,223092870,15,105,17,14,22,6469693230,42,200560490130,10,39,19,

%U 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 a(n) = A097248(A108951(n)).

%H Antti Karttunen, <a href="/A283478/b283478.txt">Table of n, a(n) for n = 1..1024</a>

%F a(n) = A097248(A108951(n)).

%F Other identities:

%F For all n >= 0, a(A019565(n)) = A283475(n).

%t 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 (PARI)

%o A034386(n) = prod(i=1, primepi(n), prime(i));

%o 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 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 A097248(n) = { my(k=A097246(n)); while(k<>n, n = k; k = A097246(k)); k; };

%o A283478(n) = A097248(A108951(n));

%o (Scheme) (define (A283478 n) (A097248 (A108951 n)))

%o (Python)

%o from sympy import primerange, factorint, nextprime

%o from operator import mul

%o def P(n): return reduce(mul, [i for i in primerange(2, n + 1)])

%o def a108951(n):

%o f = factorint(n)

%o return 1 if n==1 else reduce(mul, [P(i)**f[i] for i in f])

%o def a097246(n):

%o f=factorint(n)

%o return 1 if n==1 else reduce(mul, [(nextprime(i)**int(f[i]/2))*(i**(f[i]%2)) for i in f])

%o def a097248(n):

%o k=a097246(n)

%o while k!=n:

%o n=k

%o k=a097246(k)

%o return k

%o def a(n): return a097248(a108951(n)) # _Indranil Ghosh_, May 15 2017

%Y Cf. A019565, A097248, A108951, A283475.

%K nonn

%O 1,2

%A _Antti Karttunen_, Mar 16 2017