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

1,1

Links

Table of n, a(n) for n=1..20.

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)).

Example

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).

Prog

(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), ", "); ); }

Crossrefs

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

Sequence in context: A298272 A000438 A061109 * A219014 A341873 A013784

Adjacent sequences: A321980 A321981 A321982 * A321984 A321985 A321986

Keyword

nonn

Author

Michel Marcus, Nov 23 2018

Status

approved