A375287 Square array T(n, k), n > 1 and k >= 1, read by upward antidiagonals, 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.

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, 323, 223092870, 65893166030, 30989984674, 7933641735, 129963314, 2713332, 10280, 141

Offset

2,1

Comments

All positive terms are composite.

Links

Table of n, a(n) for n=2..37.

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

Cf. A001221, A002110 (col 1), A006049, A006073, A045932-A045938, A064709 (row 2), A185032 (row 3), A185042 (row 4), A384507 (row 5).

Sequence in context: A367665 A309253 A260017 * A351773 A123624 A287733

Adjacent sequences: A375284 A375285 A375286 * A375288 A375289 A375290

Keyword

sign,tabl

Author

Jean-Marc Rebert, Aug 10 2024

Extensions

a(29) corrected by and a(30)-a(37) from Jinyuan Wang, Sep 05 2025

Status

approved