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A366388
The number of edges minus the number of leafs in the rooted tree with Matula-Goebel number n.
6
0, 0, 1, 0, 2, 1, 1, 0, 2, 2, 3, 1, 2, 1, 3, 0, 2, 2, 1, 2, 2, 3, 3, 1, 4, 2, 3, 1, 3, 3, 4, 0, 4, 2, 3, 2, 2, 1, 3, 2, 3, 2, 2, 3, 4, 3, 4, 1, 2, 4, 3, 2, 1, 3, 5, 1, 2, 3, 3, 3, 3, 4, 3, 0, 4, 4, 2, 2, 4, 3, 3, 2, 3, 2, 5, 1, 4, 3, 4, 2, 4, 3, 4, 2, 4, 2, 4, 3, 2, 4, 3, 3, 5, 4, 3, 1, 5, 2, 5, 4, 3, 3, 4, 2, 4
OFFSET
1,5
COMMENTS
Number of iterations of A366385 needed to reach the nearest power of 2.
FORMULA
Totally additive with a(2) = 0, and for n > 1, a(prime(n)) = 1 + a(n).
a(n) = A196050(n) - A109129(n).
a(2n) = a(A000265(n)) = a(n).
EXAMPLE
See illustrations in A061773.
MATHEMATICA
Array[-1 + Length@ NestWhileList[PrimePi[#2]*#1/#2 & @@ {#, FactorInteger[#][[-1, 1]]} &, #, ! IntegerQ@ Log2[#] &] &, 105] (* Michael De Vlieger, Oct 23 2023 *)
PROG
(PARI) A366388(n) = if(n<=2, 0, if(isprime(n), 1+A366388(primepi(n)), my(f=factor(n)); (apply(A366388, f[, 1])~ * f[, 2])));
(PARI)
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
A366385(n) = { my(gpf=A006530(n)); primepi(gpf)*(n/gpf); };
A366388(n) = if(n && !bitand(n, n-1), 0, 1+A366388(A366385(n)));
CROSSREFS
Cf. A109129 (gives the exponent of the nearest power of 2 reached), A196050 (distance to the farthest power of 2, which is 1).
Cf. also A329697, A331410.
Sequence in context: A347386 A331410 A336928 * A114638 A123340 A360455
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 23 2023
STATUS
approved