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A375287
Square array T(n, k), n > 1 and k >= 1, read by antidiagonals in ascending order, give the smallest number that starts a sequence of exactly k consecutive numbers, each having exactly n distinct prime factors (counted without multiplicity), or -1 if no such number exists.
0
6, 30, 14, 210, 230, 20, 2310, 7314, 644, 33, 30030, 254540, 37960, 1308, 54, 510510, 11243154, 1042404, 134043, 2664, 91, 9699690, 965009045, 323567034, 21871365, 357642, 6850, 142
OFFSET
2,1
COMMENTS
All positive terms are composite.
FORMULA
T(n,1) = A002110(n) for n > 1.
EXAMPLE
T(2,3) = 20 = 2^2 * 5, because both 21 and 22 have the same omega. Thus, 20 is the starting number of a run of 3 numbers that each have same omega, i.e. 2. No lesser number has this property, so T(2,3) = 20.
Table begins (upper left corner = T(2,1)):
6 14 20 33 ...
30 230 644 1308 ...
210 7314 37960 134043 ...
2310 254540 1042404 21871365 ...
30030 11243154 323567034 7933641735 ...
... ... ... ... ...
CROSSREFS
Sequence in context: A367665 A309253 A260017 * A351773 A123624 A287733
KEYWORD
sign,tabl,more
AUTHOR
Jean-Marc Rebert, Aug 10 2024
STATUS
approved