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A285102 a(n) = A007913(A285101(n)). 6

%I

%S 2,6,210,72930,620310,278995269860970,12849025509071310,

%T 492608110538467706074890,1342951001046021018427857601026746070,

%U 37793589449865555275592120894959094883390892772270,728982633030274864467458719371654181886452163442582606072870,28339554655955912942523491885490197708224606885407444005070

%N a(n) = A007913(A285101(n)).

%F a(0) = 2, for n > 0, a(n) = lcm(a(n-1),A242378(n,a(n-1))) / gcd(a(n-1),A242378(n,a(n-1))).

%F a(n) = A007913(A285101(n)).

%F Other identities. For all n >= 0:

%F A001221(a(n)) = A001222(a(n)) = A285103(n).

%F A048675(a(n)) = A068052(n).

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A242378(k,n) = { while(k>0,n = A003961(n); k = k-1); n; };

%o A285102(n) = { if(0==n,2,lcm(A285102(n-1),A242378(n,A285102(n-1)))/gcd(A285102(n-1),A242378(n,A285102(n-1)))); };

%o (Scheme) (definec (A285102 n) (if (zero? n) 2 (/ (lcm (A285102 (- n 1)) (A242378bi n (A285102 (- n 1)))) (gcd (A285102 (- n 1)) (A242378bi n (A285102 (- n 1)))))))

%o (Python)

%o from sympy import factorint, prime, primepi

%o from sympy.ntheory.factor_ import core

%o from operator import mul

%o def a003961(n):

%o f=factorint(n)

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

%o def a242378(k, n):

%o while k>0:

%o n=a003961(n)

%o k-=1

%o return n

%o l=[2]

%o for n in xrange(1, 12):

%o x=l[n - 1]

%o l+=[x*a242378(n, x), ]

%o print map(core, l) # _Indranil Ghosh_, Jun 27 2017

%Y Cf. A003961, A007913, A048675, A068052, A242378, A285101, A285103.

%K nonn

%O 0,1

%A _Antti Karttunen_, Apr 15 2017

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Last modified July 18 21:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)