A375160 Square array T(n, k), n >= 2 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 prime factors (counted with multiplicity), or -1 if no such number exists.

4, 8, 9, 16, 27, 33, 32, 135, 170, -1, 64, 944, 1274, 603, -1, 128, 5264, 15470, 4023, 602, -1, 256, 29888, 33614, 57967, 12122, 2522, -1, 512, 50624, 3145310, 8706123, 632148, 204323, 211673, -1

Offset

2,1

Comments

All positive terms are composite.

Links

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

Example

T(2,3) = 33 = 3*11, because both 34 and 35 have the same number of prime factors. Thus, 33 is the starting number of a run of 3 numbers that each have 2 prime factors (counted with multiplicity). No lesser number has this property, so T(2,3) = 33.
Table begins (upper left corner = T(2,1)):
   4        9       33      -1 ...
   8       27      170     603 ...
  16      135     1274    4023 ...
  32      944    15470   57967 ...
  ...     ...      ...     ... ...

Crossrefs

Cf. A002808, A062502.

Cf. Numbers m through m+k have the same number of prime divisors (with multiplicity): A045920 (k=1), A045939 (k=2), A045940 (k=3), A045941 (k=4), A045942 (k=5), A123103 (k=6), A123201 (k=7), A358017 (k=8), A358018 (k=9), A358019 (k=10).

Sequence in context: A272758 A396304 A227645 * A285438 A089042 A340093

Adjacent sequences: A375157 A375158 A375159 * A375161 A375162 A375163

Keyword

sign,tabl,more

Author

Jean-Marc Rebert, Aug 09 2024

Status

approved