A356441 - OEIS

%I #10 Aug 07 2022 20:58:23

%S 8,16,18,24,27,32,36,40,45,48,50,54,60,64,72,75,80,81,84,90,96,98,100,

%T 105,108,112,120,125,126,128,135,140,144,147,150,154,160,162,165,168,

%U 175,176,180,189,192,196,198,200,210,216,220,224,225,231,234,240,242,243

%N Numbers k such that A309892(k) < k/gpf(k), where gpf = A006530; complement of A356438.

%C k is a term if and only if k/gpf(k) > nextprime(gpf(k)), where nextprime = A151800.

%H Jianing Song, <a href="/A356441/b356441.txt">Table of n, a(n) for n = 1..13098</a> (all terms <= 50000)

%e 8 is a term since the number of steps needed to reach 0 of the iteration x -> x - gpf(x) starting at 8 is 3: 8 -> 6 -> 3 -> 0, and 3 < 8/gpf(8).

%o (PARI) isA356441(n) = if(n>1, my(p=vecmax(factor(n)[, 1])); n/p>nextprime(p+1), 0)

%Y Cf. A356438, A309892, A006530 (gpf), A151800, A076563.

%K nonn,easy

%O 1,1

%A _Jianing Song_, Aug 07 2022