|
%I #11 Aug 07 2022 22:10:38
%S 1,2,3,4,5,6,7,9,10,11,12,13,14,15,17,19,20,21,22,23,25,26,28,29,30,
%T 31,33,34,35,37,38,39,41,42,43,44,46,47,49,51,52,53,55,56,57,58,59,61,
%U 62,63,65,66,67,68,69,70,71,73,74,76,77,78,79,82,83,85
%N Numbers k such that A309892(k) = k/gpf(k), where gpf = A006530.
%C Note that A309892(k) <= k/gpf(k); these sequence lists k such that the equality holds.
%C For k >= 2, k is a term if and only if k/gpf(k) < nextprime(gpf(k)), where nextprime = A151800.
%H Jianing Song, <a href="/A356438/b356438.txt">Table of n, a(n) for n = 1..36902</a> (all terms <= 50000)
%e 15 is a term since the number of steps needed to reach 0 of the iteration x -> x - gpf(x) starting at 15 is 3: 15 -> 10 -> 5 -> 0, and 3 = 15/gpf(15).
%o (PARI) isA356438(n) = if(n>1, my(p=vecmax(factor(n)[, 1])); n/p<nextprime(p+1), 1)
%Y Other than 1, indices of 1 in A356428.
%Y Includes A000040 and A001358 as subsequences.
%Y Complement of A356441.
%Y Cf. A309892, A006530 (gpf), A151800, A076563.
%K nonn,easy
%O 1,2
%A _Jianing Song_, Aug 07 2022
|
