OFFSET
1,1
COMMENTS
The smallest k such that lpf(k) = prime(n) with Omega(k) = A001222(k) = a(n) is the product of prime(n..n+a(n)-1).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Log log scatterplot of a(n), n = 1..16384.
EXAMPLE
Table relating the first 12 terms with prime decomposition of smallest k in A377713 (or A377792) such that lpf(k) = prime(n) and Omega(k) = a(n):
n k prime factors of k a(n)
-----------------------------------------------------------------------
1 6 2 * 3 2
2 15 3 * 5 2
3 385 5 * 7 * 11 3
4 1001 7 * 11 * 13 3
5 1062347 11 * 13 * 17 * 19 * 23 5
6 2800733 13 * 17 * 19 * 23 * 29 5
7 247110827 17 * 19 * 23 * 29 * 31 * 37 6
8 595973171 19 * 23 * 29 * 31 * 37 * 41 6
9 63392725189 23 * 29 * 31 * 37 * 41 * 43 * 47 7
10 8618654420261 29 * 31 * 37 * 41 * 43 * 47 * 53 * 59 8
11 18128893780549 31 * 37 * 41 * 43 * 47 * 53 * 59 * 61 8
12 2781907990776503 37 * 41 * 43 * 47 * 53 * 59 * 61 * 67 * 71 9
MATHEMATICA
Table[j = 1; While[Times @@ Prime[Range[i + 1, i + j]] < Prime[i]^(j + 1), j++]; j, {i, 120}]
CROSSREFS
KEYWORD
nonn,easy,new
AUTHOR
Michael De Vlieger, Nov 07 2024
STATUS
approved