cp's OEIS Frontend

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.

%I A369419 #29 Apr 04 2024 10:01:12
%S A369419 18,90,150,630,1050,1470,1890,2100,6930,11550,16170,20790,23100,25410,
%T A369419 90090,150150,210210,270270,300300,330330,390390,420420,450450,
%U A369419 1531530,2552550,3573570,4594590,5105100,5615610,6636630,7147140,7657650,8678670,9189180,29099070
%N 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.
%H A369419 Michael De Vlieger, <a href="/A369419/b369419.txt">Table of n, a(n) for n = 1..10000</a>
%F A369419 This sequence is { k = m*P(i) : 3 <= m < prime(i), i > 1, m in A369361 }.
%F A369419 Intersection of A364998 and A056808.
%e A369419 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.
%e A369419 n\k    3       5       7       9      10      11
%e A369419 ------------------------------------------------
%e A369419 2:    18;
%e A369419 3:    90,    150;
%e A369419 4:   630,   1050,   1470,   1890,   2100;
%e A369419 5:  6930,  11550,  16170,  20790,  23100,  25410;
%e A369419     ...
%t A369419 P = 2; nn = 8;
%t A369419 s = Select[Range[3, Prime[nn+1]],
%t A369419   Nor[IntegerQ@ Log2[#],
%t A369419       And[EvenQ[#1], Union@ Differences@ PrimePi[#2[[All, 1]]] == {1},
%t A369419           AllTrue[Differences@ #2[[All, -1]], # <= 0 &]]] & @@
%t A369419     {#, FactorInteger[#]} &];
%t A369419 Table[P *= Prime[n]; P*TakeWhile[s, # < Prime[n + 1] &], {n, 2, nn}]
%Y A369419 Cf. A002110, A003557, A007947, A025487, A053669, A055932, A056808, A060735, A119288, A364998, A369361, A369540, A369541.
%K A369419 nonn
%O A369419 1,1
%A A369419 _Michael De Vlieger_, Mar 10 2024