A285101 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.

2, 6, 210, 3573570, 64845819350301990, 28695662573739152697846686144187168109530, 1038300112150956151877699324649731518883355380534272386781875587619359740733888844803014212990

Offset: 0

Author

Antti Karttunen, Apr 15 2017

Keywords

• nonn

Comments

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

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..9

Crossrefs

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

Cf. also A007188, A260443.

Programs

PARI

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A242378(k,n) = { while(k>0,n = A003961(n); k = k-1); n; };
A285101(n) = { if(0==n,2,A285101(n-1)*A242378(n,A285101(n-1))); };

Python

from sympy import factorint, prime, primepi
from operator import mul
from functools import reduce
def a003961(n):
    f=factorint(n)
    return 1 if n==1 else reduce(mul, [prime(primepi(i) + 1)**f[i] for i in f])
def a242378(k, n):
    while k>0:
        n=a003961(n)
        k-=1
    return n
l=[2]
for n in range(1, 7):
    x=l[n - 1]
    l.append(x*a242378(n, x))
print(l) # Indranil Ghosh, Jun 27 2017

Scheme

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

Formula

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

Other identities. For all n >= 0:

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

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

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

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