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A246344 a(0) = 16, after which, if a(n-1) = product_{k >= 1} (p_k)^(c_k), then a(n) = (1/2) * (1 + product_{k >= 1} (p_{k+1})^(c_k)), where p_k indicates the k-th prime, A000040(k).

%I A246344 #10 Aug 26 2014 01:25:19
%S A246344 16,41,22,20,32,122,101,52,77,72,338,434,611,451,280,1040,4820,7907,
%T A246344 3960,30713,15364,22577,12154,9791,4902,8108,9131,5815,4099,2056,3551,
%U A246344 2095,1474,1385,984,2903,1455,1768,4361,5869,2940,19058,18845,13227,11053,8707,4357,2182,1640,4064,15917,9432,46238
%N A246344 a(0) = 16, after which, if a(n-1) = product_{k >= 1} (p_k)^(c_k), then a(n) = (1/2) * (1 + product_{k >= 1} (p_{k+1})^(c_k)), where p_k indicates the k-th prime, A000040(k).
%C A246344 Iterates of A048673 starting from value 16.
%C A246344 Either this sequence is actually part of the cycle containing 12 (see A246342) or 16 is the smallest member of this cycle (regardless of whether this cycle is finite or infinite), which follows because all numbers 1 .. 11 are in finite cycles, and also 13 and 14 are in closed cycles and 15 is in the cycle of 12.
%H A246344 Antti Karttunen, <a href="/A246344/b246344.txt">Table of n, a(n) for n = 0..1001</a>
%F A246344 a(0) = 16, and for n >= 1, a(n) = A048673(a(n-1)).
%e A246344 Start with a(0) = 16; then after each new term is obtained by replacing each prime factor of the previous term with the next prime, to whose product is added one before it is halved:
%e A246344 16 = 2^4 = p_1^4 -> ((p_2^4)+1)/2 = (3^4 + 1)/2 = (81+1)/2 = 41, thus a(1) = 41.
%e A246344 41 = p_13 -> ((p_14)+1)/2 = (43+1)/2 = 22, thus a(2) = 22.
%o A246344 (PARI)
%o A246344 default(primelimit, 2^30);
%o A246344 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i,1] = nextprime(f[i,1]+1)); factorback(f); \\ Using code of _Michel Marcus_
%o A246344 A048673(n) = (A003961(n)+1)/2;
%o A246344 k = 16; for(n=0, 1001, write("b246344.txt", n, " ", k) ; k = A048673(k));
%o A246344 (Scheme, with memoization-macro definec)
%o A246344 (definec (A246344 n) (if (zero? n) 16 (A048673 (A246344 (- n 1)))))
%Y A246344 A246345 gives the terms of the same cycle when going to the opposite direction from 16.
%Y A246344 Cf. A048673, A064216, A246342, A246343.
%Y A246344 Cf. also A246281, A246282, A246351, A246352, A246361, A246362, A246371, A246372.
%K A246344 nonn
%O A246344 0,1
%A A246344 _Antti Karttunen_, Aug 24 2014