A384000 Smallest number k with n distinct prime factors such that A010846(k) = A024718(n) (a tight lower bound), or -1 if such k does not exist.
1, 2, 6, 1001, 268801, 3433936673, 2603508937756211
Offset: 0
Examples
Table of a(n), n = 0..6, showing prime decomposition and cardinality of row a(n) of A162306, c(n) = A010846(a(n)) = A024718(n).
n a(n) c(n) prime factors of a(n) a(n)
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0 1 1 -
1 2 2 2 A000040(1)
2 6 5 2, 3 A138109(1)
3 1001 15 7, 11, 13 A383177(1)
4 268801 50 13, 23, 29, 31 A383178(2)
5 3433936673 176 41, 83, 97, 101, 103 A383179(209)
6 2603508937756211 638 163, 373, 439, 457, 461, 463
Tables of terms m in r(a(n)) = row a(n) of A162306, writing instead only exponents i of prime power factors p^i | m for each p | a(n), written in order of the prime base:
For n = 2, i.e., squarefree semiprime k in A138109 (that achieves the lower bound), we have the following ordered exponent combinations in a rank-2 table:
00 10 20
01 11
Thus row 6 of A162306 has the following elements:
1 2 4
3 6
For n = 3, i.e., sphenic k in A383177 (that achieves the lower bound), we have the following ordered exponent combinations in a rank-3 table:
000 100 200 300 001 101 201 002
010 110 210 011 111
020 120
Thus row 1001 of A162306 has the following elements:
1 7 49 343 13 91 637 169
11 77 539 141 1001
121 857
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