A125666 Table read by ascending antidiagonals: n-th row of table consists of the positive integers divisible by exactly n distinct primes.

2, 6, 3, 30, 10, 4, 210, 42, 12, 5, 2310, 330, 60, 14, 7, 30030, 2730, 390, 66, 15, 8, 510510, 39270, 3570, 420, 70, 18, 9, 9699690, 570570, 43890, 3990, 462, 78, 20, 11, 223092870, 11741730, 690690, 46410, 4290, 510, 84, 21, 13, 6469693230, 281291010

Offset

1,1

Comments

Concatenated sequence is a permutation of the integers >= 2.

The chosen encoding of the table by *rising* antidiagonals is contrary to the OEIS standard which rather expects falling antidiagonals: as a consequence, displaying this sequence as a table (2nd link after the list of terms above) will list the integers with given number of prime divisors in columns rather than rows. - M. F. Hasler, Jun 06 2024

Links

Table of n, a(n) for n=1..47.

Example

The table begins:
  n\k|     1     2    3    4    5    6  ...
  ---+-------------------------------------
   1 |     2,    3,   4,   5,   7,   8, ...
   2 |     6,   10,  12,  14,  15, ...
   3 |    30,   42,  60,  66, ...
   4 |   210,  330, 390, ...
   5 |  2310, 2730, ...
   6 | 30030,  ...
  ...|   ...

Mathematica

f[n_, m_] := f[n, m] = Block[{c = m, k = If[m == 1, Product[Prime[i], {i, n}], f[n, m - 1] + 1]}, While[Length@FactorInteger[k] != n, k++ ]; k]; Table[f[d - m + 1, m], {d, 10}, {m, d}] // Flatten (* Ray Chandler, Feb 08 2007 *)

Prog

(PARI) A125666(n, k=0)={if(k, for(m=vecprod(primes(n)), oo, omega(m)!=n || k-- || return(m)), A125666(A004736(n), A002260(n)))} \\ M. F. Hasler, Jun 06 2024

Crossrefs

Cf. A001221, A002110 (col 1), A246655 (row 1), A007774 (row 2), A033992 (row 3), A033993 (row 4), A051270 (row 5), A074969 (row 6), A176655 (row 7), A348072 (row 8), A348073 (row 9), A073329 (diag), compare to A048692.

Sequence in context: A376413 A303761 A283478 * A371799 A307540 A304087

Adjacent sequences: A125663 A125664 A125665 * A125667 A125668 A125669

Keyword

nonn,tabl

Author

Leroy Quet, Jan 29 2007

Extensions

Extended by Ray Chandler, Feb 08 2007

Status

approved