cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A375287 #29 Aug 11 2024 11:52:28
%S A375287 6,30,14,210,230,20,2310,7314,644,33,30030,254540,37960,1308,54,
%T A375287 510510,11243154,1042404,134043,2664,91,9699690,965009045,323567034,
%U A375287 21871365,357642,6850,142
%N 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.
%C A375287 All positive terms are composite.
%F A375287 T(n,1) = A002110(n) for n > 1.
%e A375287 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 A375287 Table begins (upper left corner = T(2,1)):
%e A375287     6       14        20         33 ...
%e A375287    30      230       644       1308 ...
%e A375287   210     7314     37960     134043 ...
%e A375287  2310   254540   1042404   21871365 ...
%e A375287 30030 11243154 323567034 7933641735 ...
%e A375287   ...      ...       ...        ... ...
%Y A375287 Cf. A001221, A002110 (col 1), A002808, A006049 (row 1), A006073, A045932-A045938.
%K A375287 sign,tabl,more
%O A375287 2,1
%A A375287 _Jean-Marc Rebert_, Aug 10 2024