A324882 a(1) = 0; for n > 1, a(n) = A001511(A324866(n)), where A324866(n) = A156552(n) OR (A323243(n) - A156552(n)).

0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2

Offset: 1

Author

Antti Karttunen, Mar 28 2019

Keywords

• nonn

Comments

Terms 0 .. k occur for the first time at n = 1, 2, 9, 25, 133, 253, 559, 2159, 2489, 3151, 5597, 7967, ..., which after 2 seem all to be semiprimes, that is, A156552(n) has binary weight 2.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A001511, A156552, A323243, A324866, A324883, A324884.

Programs

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
A324866(n) = { my(k=A156552(n)); bitor(k,(A323243(n)-k)); }; \\ Needs also code 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.
A324882(n) = A001511ext(A324866(n));

Formula

a(1) = 0; for n > 1, a(n) = A001511(A324866(n)).

a(n) = A324884(n) - A324883(n).

a(p) = 1 for all primes p.