A389449 - OEIS

%I #10 Dec 02 2025 21:26:33

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

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

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

%N a(n) = 1 if A260443(A048675(n)) = n, otherwise 0.

%C Question: Does this sequence have an asymptotic mean?

%H Antti Karttunen, <a href="/A389449/b389449.txt">Table of n, a(n) for n = 1..65537</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 related to prime indices in the factorization of n</a>.

%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>.

%o (PARI)

%o A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };

%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(1+f[i, 1])); factorback(f); };

%o A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2))));

%o A055396(n) = if(n==1, 0, primepi(factor(n)[1, 1]));

%o A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));

%o A389449(n) = ((1==n) || isprime(n) || ((omega(n) == 1+(A061395(n)-A055396(n))) && (A260443(A048675(n)) == n))); \\ Somewhat optimized.

%Y Characteristic function of A260442.

%Y Cf. A048675, A260443.

%K nonn

%O 1

%A _Antti Karttunen_, Dec 02 2025