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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 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 CROSSREFS Cf. A001222, A003961, A007913, A028362, A048675, A053632, A068052, A242378, A248663, A285102. Cf. also A007188, A260443. Sequence in context: A333944 A091439 A285102 * A361086 A176782 A357191 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 8 13:24 EDT 2023. Contains 363165 sequences. (Running on oeis4.)