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%I #23 Mar 31 2018 16:56:27
%S 4,11,23,257,13007,44512049,46880563785749,
%T 125637016478802067649031191,
%U 652182699863469019760217209096329987925268834143233,1800254420479597976179975458181139131985404009703136640765845238082635790500153934999846722641241849
%N a(n) = nextprime(1/(2/sigma[-1](P(n)) - 1)) where P(n) = Product_{0 <= k < n} a(k), sigma[-1](x) = sigma(x)/x, a(0) = 4.
%C Here, nextprime(x) = min { p > x; p prime }, prevprime(x) = max { p < x; p prime }.
%C The next term, a(10) ~ 3.1*10^196, is too large to be displayed above.
%C From a(3) on, a(n+1) has roughly twice the number of digits of a(n).
%C For n >= 1, a(n) is the least prime such that Product_{k=0..n} a(k) is deficient. This implies that (Product_{k=0..n-1} a(k))*prevprime(a(n)) is perfect for n = 1, and a primitive weird number (A002975) for some but not all larger n.
%H M. F. Hasler, <a href="/A295001/b295001.txt">Table of n, a(n) for n = 0..13</a>
%e Let Q(x) = 1/(2/sigma[-1](x) - 1), P(n) = Product(a(k), k=0..n-1), and start with a(0) = 4 = P(1). Then:
%e Q(P(1)) = 7, a(1) = 11. (4*7 is perfect, P(2) = 4*11 is deficient.)
%e Q(P(2)) = 21, a(2) = 23. (4*11*19 is weird, P(3) = 4*11*23 is deficient.)
%e Q(P(3)) = 252, a(3) = 257. (P(3)*251 is weird, P(4) = 4*11*23*257 is deficient.)
%e Q(P(4)) = 13003.2, a(4) = 13007. (P(4)*13003 is weird, P(5) = 4*11*23*257*13007 is deficient.)
%e Q(P(5)) = 44512006.7..., a(5) = 44512049. (P(5)*44511949 is weird ; P(6) = 4*11*257*44512049 is deficient.)
%e P(6)*prevprime(a(6)) is semiperfect, i.e., no more weird.
%o (PARI) A295001=List(m=4);for(n=1,13,listput(A295001,p=nextprime(1\(2/sigma(m,-1)-1)+1));p>default(primelimit)&&addprimes(p);m*=p)
%Y Cf. A002975 (primitive weird numbers), A000203 (sigma).
%Y The nextprime and prevprime functions are here used for possibly non-integral arguments, but rounding these down or up allows the use of the nextprime and prevprime functions for integer arguments, A151800 and A151799.
%Y See A262228 for the variant starting with a(0) = 1.
%K nonn,hard
%O 0,1
%A _M. F. Hasler_, Nov 23 2017
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