OFFSET
0,2
COMMENTS
Smallest k such that there are exactly n primes p such that gpf(k+p) = p (such p must be prime factors of k).
Smallest k having exactly n distinct prime factors p such that k+p is p-smooth.
Conjectures (if no term equals -1): (Start)
(1) Sequence is strictly increasing.
(2) All terms are squarefree.
(3) All terms are in A354525. (End)
EXAMPLE
a(4) = 1660577: 1660577 = 17*23*31*127, and we have 1660577+17 = 2*13^2*17^3 is 17-smooth, 1660577+23 = 2^3*5^2*19^2*23 is 23-smooth, 1660577+31 = 2^6*3^3*31^2 is 31-smooth, 1660577+137 = 2*11*19*29*137, so m - gpf(m) = 1660577 has 4 solutions m = 1660577+17 = 1660594, 1660577+23 = 1660600, 1660577+31 = 1660608, and 1660577+137 = 1660714.
PROG
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Jianing Song, Aug 16 2022
STATUS
approved