A324883 a(n) = 1 if A055396(n) < A324885(n), otherwise 0.

0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1

Offset

1

Comments

Difference between the 2-adic valuations of A324819(n) and A324866(n).

Of the first 10000 terms, 2540 are 0's and 7460's are 1's. Even n such that a(n) = 0 are rare: 2, 10, 50, 98, 154, 266, 374, 598, 770, 1054, 1250, 1558, 2162, 2662, 3422, 4154, 5390, 5402, 6578, 6806, 8342, 8918, 9682 are all such n less than 10001.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)

Index entries for characteristic functions

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A324884(n) - A324882(n).

For n > 1, a(n) = A007814(A324819(n)) - A007814(A324866(n)).

For n > 1, a(n) = A324903(A156552(n)).

a(p) = 0 for all primes p.

Prog

(PARI)
\\ Needs code also from A323243.
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));
A324866(n) = { my(k=A156552(n)); bitor(k, (A323243(n)-k)); };
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));
A324884(n) = A001511ext(A324819(n));
A324883(n) = (A324884(n)-A324882(n));

Crossrefs

Cf. A001511, A007814, A055396, A156552, A323243, A324819, A324866, A324882, A324884, A324885, A324903.

Sequence in context: A099618 A361496 A360125 * A106002 A341612 A252742

Adjacent sequences: A324880 A324881 A324882 * A324884 A324885 A324886

Keyword

nonn

Author

Antti Karttunen, Mar 28 2019

Status

approved