A369419 Numbers k that are neither squarefree nor prime powers such that A119288(k) <= k/A007947(k) < A053669(k) and A007947(k) is not a primorial.

18, 90, 150, 630, 1050, 1470, 1890, 2100, 6930, 11550, 16170, 20790, 23100, 25410, 90090, 150150, 210210, 270270, 300300, 330330, 390390, 420420, 450450, 1531530, 2552550, 3573570, 4594590, 5105100, 5615610, 6636630, 7147140, 7657650, 8678670, 9189180, 29099070

Offset: 1

Author

Michael De Vlieger, Mar 10 2024

Keywords

• nonn

Examples

			Seen as an irregular triangle T(n,k) of rows n where T(n,k) = P(n)*k, and k < prime(n+1) is in A369361.
n\k    3       5       7       9      10      11
------------------------------------------------
2:    18;
3:    90,    150;
4:   630,   1050,   1470,   1890,   2100;
5:  6930,  11550,  16170,  20790,  23100,  25410;
    ...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A003557, A007947, A025487, A053669, A055932, A056808, A060735, A119288, A364998, A369361, A369540, A369541.

Programs

Mathematica

P = 2; nn = 8;
s = Select[Range[3, Prime[nn+1]],
  Nor[IntegerQ@ Log2[#],
      And[EvenQ[#1], Union@ Differences@ PrimePi[#2[[All, 1]]] == {1},
          AllTrue[Differences@ #2[[All, -1]], # <= 0 &]]] & @@
    {#, FactorInteger[#]} &];
Table[P *= Prime[n]; P*TakeWhile[s, # < Prime[n + 1] &], {n, 2, nn}]

Formula

This sequence is { k = m*P(i) : 3 <= m < prime(i), i > 1, m in A369361 }.

Intersection of A364998 and A056808.