A375287 - OEIS

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.

%I #29 Aug 11 2024 11:52:28

%S 6,30,14,210,230,20,2310,7314,644,33,30030,254540,37960,1308,54,

%T 510510,11243154,1042404,134043,2664,91,9699690,965009045,323567034,

%U 21871365,357642,6850,142

%N 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.

%C All positive terms are composite.

%F T(n,1) = A002110(n) for n > 1.

%e 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.

%e Table begins (upper left corner = T(2,1)):

%e 6 14 20 33 ...

%e 30 230 644 1308 ...

%e 210 7314 37960 134043 ...

%e 2310 254540 1042404 21871365 ...

%e 30030 11243154 323567034 7933641735 ...

%e ... ... ... ... ...

%Y Cf. A001221, A002110 (col 1), A002808, A006049 (row 1), A006073, A045932-A045938.

%K sign,tabl,more

%O 2,1

%A _Jean-Marc Rebert_, Aug 10 2024