A288784 Irregular triangle read by rows: T(n,m) is the list of numbers k*A002110(n) <= k*t < (k + 1)*A002110(n) such that A001222(k*t) = n, with 1 <= k < prime(n + 1).

1, 2, 3, 4, 6, 10, 12, 18, 24, 30, 42, 60, 84, 90, 120, 150, 180, 210, 330, 390, 420, 630, 840, 1050, 1260, 1470, 1680, 1890, 2100, 2310, 2730, 3570, 3990, 4290, 4620, 5460, 6930, 8190, 9240, 10920, 11550, 13650, 13860, 16170, 18480, 20790, 23100, 25410, 27720

Offset

0,2

Comments

A060735 and A002110 are subsets.

This sequence is a necessary but insufficient condition for A244052. Terms that are in A060735 and A002110 are also in A244052. The first terms of this sequence that are not in A244052 are {3, 4290, 881790, 903210, 1009470, 17160990, 363993630, 380570190, 406816410, 434444010, ...}.

Primorial p_n# = A002110(n) is the smallest squarefree number with n prime factors. Consider the list of squarefree numbers t with n prime factors greater than and including A002110(n) but less than 2*A002110(n). Extend the list to include products k*t of this list with 1 <= k < prime(n+1) such that k*t < (k+1)*p_n#. This list contains squarefree numbers k*t with n distinct primes and presumes that the number (k+1)*p_n# serves as a "limit" beyond which k*t > (k+1)p_n# are not in the sequence.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..11793 (rows 1 <= n <= 30).

Michael De Vlieger, Terms of a(n) with 1 <= n <= 653 in A002110, A060735, and A244052

Eric Weisstein's World of Mathematics, Primorial

Eric Weisstein's World of Mathematics, Squarefree

Example

Triangle begins:
    n   T(n,m)
    0:   1;
    1:   2,  3,  4;
    2:   6, 10, 12, 18, 24;
    3:  30, 42, 60, 84, 90, 120, 150, 180;
       ...

Mathematica

Table[Function[P, Function[s, Flatten@ Map[Function[k, Select[k s, # < (k + 1) P &]], Range[1, Prime[n + 1] - 1]]]@ Select[Range[P, 2 P - 1], And[SquareFreeQ@ #, PrimeOmega@ # == n] &]]@ Product[Prime@ i, {i, n}], {n, 0, 5}] (* Michael De Vlieger, Jun 15 2017 *)

Crossrefs

Cf. A001221, A002110, A005117, A006881, A033992, A060735, A244052.

Sequence in context: A181312 A373320 A330006 * A322164 A237823 A241547

Adjacent sequences: A288781 A288782 A288783 * A288785 A288786 A288787

Keyword

nonn,tabf

Author

Michael De Vlieger, Jun 15 2017

Status

approved