cp's OEIS Frontend

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

%I A285102 #17 Apr 21 2021 12:08:35
%S A285102 2,6,210,72930,620310,278995269860970,12849025509071310,
%T A285102 492608110538467706074890,1342951001046021018427857601026746070,
%U A285102 37793589449865555275592120894959094883390892772270,728982633030274864467458719371654181886452163442582606072870,28339554655955912942523491885490197708224606885407444005070
%N A285102 a(n) = A007913(A285101(n)).
%F A285102 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 A285102 a(n) = A007913(A285101(n)).
%F A285102 Other identities. For all n >= 0:
%F A285102 A001221(a(n)) = A001222(a(n)) = A285103(n).
%F A285102 A048675(a(n)) = A068052(n).
%o A285102 (PARI)
%o A285102 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A285102 A242378(k,n) = { while(k>0,n = A003961(n); k = k-1); n; };
%o A285102 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 A285102 (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 A285102 (Python) # uses [A003961, A242378]
%o A285102 from sympy import factorint, prime, primepi
%o A285102 from sympy.ntheory.factor_ import core
%o A285102 from operator import mul
%o A285102 def a003961(n):
%o A285102     f=factorint(n)
%o A285102     return 1 if n==1 else reduce(mul, [prime(primepi(i) + 1)**f[i] for i in f])
%o A285102 def a242378(k, n):
%o A285102     while k>0:
%o A285102         n=a003961(n)
%o A285102         k-=1
%o A285102     return n
%o A285102 l=[2]
%o A285102 for n in range(1, 12):
%o A285102     x=l[n - 1]
%o A285102     l.append(x*a242378(n, x))
%o A285102 print([core(j) for j in l]) # _Indranil Ghosh_, Jun 27 2017
%Y A285102 Cf. A003961, A007913, A048675, A068052, A242378, A285101, A285103.
%K A285102 nonn
%O A285102 0,1
%A A285102 _Antti Karttunen_, Apr 15 2017