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%I #16 Aug 11 2022 03:20:00
%S 1,4,8,25,50,108,169,243,256,338,486,512,729,768,972,1024,1156,1215,
%T 2312,3375,5000,7921,8192,8748,10000,12800,15000,15842,20000,25000,
%U 50176,54289,85184,88209,100352,104976,108578,131072,176418,177147
%N Numbers k that divide A000201(k)^m for some integer m > 0, where A000201 is the lower Wythoff sequence.
%C Let k = p_1^{e_1} * p_2^{e_2} * ... * p_r^{e_r}. Then k is in this sequence iff p_1*p_2*...*p_r divides A000201(k).
%C Many of these terms are powers of Fibonacci numbers.
%C Perhaps this is expected, since A000201(k) involves floor(k*phi).
%e For n=8, A000201(8)=12. Since 8 divides 12^2, 8 is in this sequence.
%e For n=9, A000201(9)=14. Since 9 cannot divide 14^m for any m, 9 is not in this sequence.
%o (Python)
%o from math import isqrt, prod
%o from itertools import count, islice
%o from sympy import primefactors
%o def A185615_gen(startvalue=1): # generator of terms >= startvalue
%o return filter(lambda n: not (n+isqrt(5*n**2)>>1)%prod(primefactors(n)),count(max(startvalue,1)))
%o A185615_list = list(islice(A185615_gen(),30)) # _Chai Wah Wu_, Aug 10 2022
%Y Cf. A000201, A185616, A185617.
%K nonn
%O 1,2
%A _Paul D. Hanna_ and _Sean A. Irvine_, Jan 31 2011
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