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A324884
a(1) = 0; for n > 1, a(n) = A001511(A324819(n)), where A324819(n) = 2*A156552(n) OR A323243(n).
4
0, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 1, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 3, 2, 1, 2, 4, 2, 3, 2, 1, 2, 1, 2, 2, 2, 3, 2, 1, 1, 3, 2, 1, 2, 1, 2, 3
OFFSET
1,4
COMMENTS
Terms 0 .. k occur for the first time at n = 1, 2, 4, 9, 85, 133, 451, 1469, 2159, 2489, 4393, 7279, ..., which after 2 seem all to be semiprimes, that is, A156552(n) has binary weight 2.
FORMULA
a(1) = 0; for n > 1, a(n) = A001511(A324819(n)).
a(n) = A324882(n) + A324883(n).
a(p) = 1 for all primes p.
PROG
(PARI)
A156552(n) = {my(f = factor(n), 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
A324819(n) = bitor(2*A156552(n), A323243(n)); \\ Needs code also from A323243.
A001511ext(n) = if(!n, n, sign(n)*(1+valuation(n, 2))); \\ Like A001511 but gives 0 for 0 and -A001511(-n) for negative numbers.
A324884(n) = A001511ext(A324819(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 28 2019
STATUS
approved