A285101 - OEIS

%I #25 May 07 2021 10:42:25

%S 2,6,210,3573570,64845819350301990,

%T 28695662573739152697846686144187168109530,

%U 1038300112150956151877699324649731518883355380534272386781875587619359740733888844803014212990

%N a(0) = 2, for n > 0, a(n) = a(n-1)*A242378(n,a(n-1)), where A242378(n,a(n-1)) shifts the prime factorization of a(n-1) n primes towards larger primes with A003961.

%C Multiplicative encoding of irregular table A053632 (in style of A007188 and A260443).

%H Indranil Ghosh, <a href="/A285101/b285101.txt">Table of n, a(n) for n = 0..9</a>

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

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

%F A001222(a(n)) = A000079(n).

%F A048675(a(n)) = A028362(1+n).

%F A248663(a(n)) = A068052(n).

%F A007913(a(n)) = A285102(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 A285101(n) = { if(0==n,2,A285101(n-1)*A242378(n,A285101(n-1))); };

%o (Scheme) (definec (A285101 n) (if (zero? n) 2 (* (A285101 (- n 1)) (A242378bi n (A285101 (- n 1)))))) ;; For A242378bi see A242378.

%o (Python)

%o from sympy import factorint, prime, primepi

%o from operator import mul

%o from functools import reduce

%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 range(1, 7):

%o     x=l[n - 1]

%o     l.append(x*a242378(n, x))

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

%Y Cf. A001222, A003961, A007913, A028362, A048675, A053632, A068052, A242378, A248663, A285102.

%Y Cf. also A007188, A260443.

%K nonn

%O 0,1

%A _Antti Karttunen_, Apr 15 2017