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.

6, 6501, 526809, 419709, 5116053, 14923101, 397013259, 441623073, 2276169717, 1290664569, 38449648947, 112155723039, 122976253119, 507181098441, 25104075429, 525044080551, 2801263972359, 11894687774967, 8825968853913, 27500380094379

Offset: 1

Author

Michel Marcus, Nov 23 2018

Keywords

• nonn

Examples

			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).
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)
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).
		

Crossrefs

Cf. A001414, A056240, A151799, A293652, A295185.

Programs

PARI

sopfr(k) = my(f=factor(k)); sum(j=1, #f~, f[j, 1]*f[j, 2]); \\ A001414
isok(k, n) = sopfr(k) == n;
a056240(n) = my(k=2); while(!isok(k, n), k++); k;
a(p, n) = {newp = p; for (k=1, n, newp = precprime(newp-1)); newp*a056240(p-newp);}
lista() = {vp = [5, 211, 4327, 4547, ...,  ]; /* A293652 */ for (n=1, #vp, print1(chk(vp[n], n), ", "););}

Formula

a(n) = q*A056240(p-q) where p = A293652(n) and q = A151799^n(p) where A151799^n is A151799(A151799(...)) repeated n times.

a(n) = A295185(A293652(n)).