A373585 a(n) = 1 if A373149(n) is even, otherwise 0, where A373149 is fully additive with a(2) = 1 and a(p) = prevprime(p) for odd primes p.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Formula

a(n) = A059841(A373149(n)).

a(n) = A059841(A001222(n) - A007949(n)).

Mathematica

Array[Boole[EvenQ[PrimeOmega[#] - IntegerExponent[#, 3]]] &, 100] (* Paolo Xausa, Dec 17 2024 *)

Prog

(PARI)
A373149(n) = { my(f = factor(n)); sum(i = 1, #f~, f[i, 2]*if(2==f[i, 1], 1, precprime(f[i, 1] - 1))); };
A373585(n) = !(A373149(n)%2);
(PARI) A373585(n) = !((bigomega(n)-valuation(n, 3))%2);

Crossrefs

Characteristic function of A373586, whose complement A373587 gives the positions of 0's.

Cf. A001222, A007949, A059841, A373149.

Sequence in context: A145377 A374113 A374107 * A246260 A275973 A218173

Adjacent sequences: A373582 A373583 A373584 * A373586 A373587 A373588

Keyword

nonn

Author

Antti Karttunen, Jun 12 2024

Status

approved