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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. 7
2, 6, 210, 3573570, 64845819350301990, 28695662573739152697846686144187168109530, 1038300112150956151877699324649731518883355380534272386781875587619359740733888844803014212990 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

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).

PROG

(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))); };

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

(Python)

from sympy import factorint, prime, primepi

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 xrange(1, 7):

    x=l[n - 1]

    l+=[x*a242378(n, x), ]

print l # Indranil Ghosh, Jun 27 2017

CROSSREFS

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

Cf. also A007188, A260443.

Sequence in context: A156517 A091439 A285102 * A176782 A013083 A110387

Adjacent sequences:  A285098 A285099 A285100 * A285102 A285103 A285104

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 15 2017

STATUS

approved

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Last modified June 25 17:47 EDT 2019. Contains 324353 sequences. (Running on oeis4.)