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

2, 6, 210, 72930, 620310, 278995269860970, 12849025509071310, 492608110538467706074890, 1342951001046021018427857601026746070, 37793589449865555275592120894959094883390892772270, 728982633030274864467458719371654181886452163442582606072870, 28339554655955912942523491885490197708224606885407444005070

Offset: 0

Author

Antti Karttunen, Apr 15 2017

Keywords

• nonn

Crossrefs

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

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

Python

# uses [A003961, A242378]
from sympy import factorint, prime, primepi
from sympy.ntheory.factor_ import core
from operator import mul
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, 12):
    x=l[n - 1]
    l.append(x*a242378(n, x))
print([core(j) for j in l]) # Indranil Ghosh, Jun 27 2017

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)))))))

Formula

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))).

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

Other identities. For all n >= 0:

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

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