A364955 a(n) = A252464(n) - A364954(n), where A364954(n) is the length of the common prefix in the binary expansions of A156552(n) and A156552(A163511(n)).

0, 0, 0, 0, 2, 0, 1, 0, 1, 3, 4, 0, 4, 2, 2, 0, 6, 2, 7, 4, 4, 5, 8, 0, 3, 5, 3, 3, 7, 3, 6, 0, 5, 7, 4, 3, 11, 8, 6, 5, 12, 5, 13, 6, 4, 9, 14, 0, 4, 4, 6, 6, 14, 4, 4, 4, 6, 8, 14, 4, 14, 7, 3, 0, 6, 6, 18, 8, 9, 5, 19, 4, 20, 12, 3, 9, 5, 7, 21, 6, 3, 13, 22, 6, 7, 14, 10, 7, 23, 5, 6, 10, 11, 15, 8, 0, 23, 5, 5, 5

Offset

1,5

Links

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

Prog

(PARI)
Abincompreflen(n, m) = { my(x=binary(n), y=binary(m), u=min(#x, #y)); for(i=1, u, if(x[i]!=y[i], return(i-1))); (u); };
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A364954(n) = Abincompreflen(A156552(n), A156552(A163511(n)));
A061395(n) = if(n>1, primepi(vecmax(factor(n)[, 1])), 0);
A252464(n) = if(1==n, 0, (bigomega(n) + A061395(n) - 1));
A364955(n) = (A252464(n)-A364954(n));

Crossrefs

Cf. A156552, A163511, A364954, A364956 (positions of 0's).

Cf. also A364570.

Sequence in context: A004173 A185370 A352747 * A112517 A112519 A276981

Adjacent sequences: A364952 A364953 A364954 * A364956 A364957 A364958

Keyword

nonn

Author

Antti Karttunen, Sep 02 2023

Status

approved