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Characteristic function of A347242.
7

%I #9 Feb 10 2022 20:06:04

%S 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,

%T 0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,

%U 0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,0,1

%N Characteristic function of A347242.

%H Antti Karttunen, <a href="/A347244/b347244.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(1) = 0, and for n > 1, a(n) = 1 if for some k > 0, A006530(A000593^(k)(n)) >= A006530(n), otherwise 0. Here A000593^(k) means the k-fold application of the sum of odd divisors.

%F For n >= 1, a(n) = 0 iff A347245(n) = 0.

%o (PARI)

%o A000265(n) = (n >> valuation(n, 2));

%o A000593(n) = sigma(A000265(n));

%o A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);

%o A347244(n) = { my(gpf=A006530(n)); while(n>1, n = A000593(n); if(A006530(n)>=gpf,return(1))); (0); };

%Y Cf. A000593, A006530, A347240, A347242, A347243, A347245, A347246.

%K nonn

%O 1

%A _Antti Karttunen_, Aug 28 2021