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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)).
3
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 02 2023
STATUS
approved