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A321983 Let p be A293652(n), a(n) is the smallest composite number whose greatest prime factor is the n-th prime below p and whose prime factors add up to p.

%I A321983 #10 Nov 23 2018 05:32:29
%S A321983 6,6501,526809,419709,5116053,14923101,397013259,441623073,2276169717,
%T A321983 1290664569,38449648947,112155723039,122976253119,507181098441,
%U A321983 25104075429,525044080551,2801263972359,11894687774967,8825968853913,27500380094379
%N A321983 Let p be A293652(n), a(n) is the smallest composite number whose greatest prime factor is the n-th prime below p and whose prime factors add up to p.
%F A321983 a(n) = q*A056240(p-q) where p = A293652(n) and q = A151799^n(p) where A151799^n is A151799(A151799(...)) repeated n times.
%F A321983 a(n) = A295185(A293652(n)).
%e A321983 a(1) = 6 since 6 = 3 * 2, the smallest composite number whose prime divisors add to 5, is a multiple of 3, the greatest prime < 5, where 5 = A293652(1).
%e A321983 a(2) = 6501 since 6501 = 3 * 11 * 197, the smallest composite whose prime divisors add to 211, and 197 < 199 < 211 is the second prime below 211, where 211 = A293652(2)
%e A321983 a(3) = 526809 since 526809 = 3 * 41 * 4283, the smallest composite whose prime divisors add to 4327, and 4283 < 4289 < 4297 < 4327 is the third prime below 4327, where 4327 = A293652(3).
%o A321983 (PARI) sopfr(k) = my(f=factor(k)); sum(j=1, #f~, f[j, 1]*f[j, 2]); \\ A001414
%o A321983 isok(k, n) = sopfr(k) == n;
%o A321983 a056240(n) = my(k=2); while(!isok(k, n), k++); k;
%o A321983 a(p, n) = {newp = p; for (k=1, n, newp = precprime(newp-1)); newp*a056240(p-newp);}
%o A321983 lista() = {vp = [5, 211, 4327, 4547, ...,  ]; /* A293652 */ for (n=1, #vp, print1(chk(vp[n], n), ", "););}
%Y A321983 Cf. A001414, A056240, A151799, A293652, A295185.
%K A321983 nonn
%O A321983 1,1
%A A321983 _Michel Marcus_, Nov 23 2018