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a(n) = 1 if n is odd and A064989(sigma(n)) > A064989(n), otherwise 0. Here A064989 shifts the prime factorization one step towards lower primes, and sigma is the sum of divisors function.
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%I #10 May 05 2022 10:07:56

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

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

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

%N a(n) = 1 if n is odd and A064989(sigma(n)) > A064989(n), otherwise 0. Here A064989 shifts the prime factorization one step towards lower primes, and sigma is the sum of divisors function.

%H Antti Karttunen, <a href="/A353639/b353639.txt">Table of n, a(n) for n = 1..100000</a>

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

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F For n > 1, a(n) = A000035(n) * (1-A348737(A064989(n))) = A000035(n) - A353638(n). [Conjectured, see comments in A336702]

%o (PARI)

%o A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };

%o A353639(n) = ((n%2) && (A064989(sigma(n))>A064989(n)));

%Y Characteristic function of A348749 (see also A348739).

%Y Cf. A000035, A000203, A064989, A336702, A348737, A353638.

%K nonn

%O 1

%A _Antti Karttunen_, May 04 2022