A389449 a(n) = 1 if A260443(A048675(n)) = n, otherwise 0.

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, 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, 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

Offset

1

Comments

Question: Does this sequence have an asymptotic mean?

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions.

Index entries for sequences related to prime indices in the factorization of n.

Index entries for sequences related to Stern's sequences.

Prog

(PARI)
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(1+f[i, 1])); factorback(f); };
A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2))));
A055396(n) = if(n==1, 0, primepi(factor(n)[1, 1]));
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A389449(n) = ((1==n) || isprime(n) || ((omega(n) == 1+(A061395(n)-A055396(n))) && (A260443(A048675(n)) == n))); \\ Somewhat optimized.

Crossrefs

Characteristic function of A260442.

Cf. A048675, A260443.

Sequence in context: A189206 A323152 A192280 * A380467 A380524 A342005

Adjacent sequences: A389446 A389447 A389448 * A389450 A389451 A389452

Keyword

nonn

Author

Antti Karttunen, Dec 02 2025

Status

approved