A336923 a(n) = 1 if sigma(2n) - sigma(n) is a power of 2, otherwise 0.

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

Offset

1

Comments

a(n) = 1 if n is a squarefree product of Mersenne primes (A000668) multiplied by a power of 2, otherwise 0.

c(n) = a(n)*A000035(n) is the characteristic function of A046528.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Formula

a(n) = A209229(A062731(n)-A000203(n)).

a(n) = 1 iff A336922(n) = 0, i.e., when A331410(n) is equal to A005087(n).

From Antti Karttunen, Jan 08 2023: (Start)

Multiplicative with a(2^e) = 1, and for odd primes p, a(p^e) = A209229(p+1) if e = 1, and 0 if e > 1.

Multiplicative with a(p^e) = [p==2] + (A036987(p)*[e==1]), where [ ] is the Iverson bracket.

a(n) = A209229(A002131(n)) = A209229(A054785(n)).

(End)

Prog

(PARI)
A209229(n) = (n && !bitand(n, n-1));
A336923(n) = A209229(sigma(n+n)-sigma(n));
(PARI) A336923(n) = { my(f=factor(n)); prod(k=1, #f~, (2==f[k, 1] || A209229(f[k, 1]+1)*(1==f[k, 2]))); }; \\ Antti Karttunen, Jan 06 2023

Crossrefs

Characteristic function of A054784.

Cf. A000035, A000203, A000668, A002131, A005087, A036987, A046528, A054785, A062731, A209229, A331410, A335430, A336922, A359579 (Dirichlet inverse).

Cf. also A336477 (analogous sequence for Fermat primes).

Sequence in context: A115954 A115526 A363343 * A239681 A054524 A110471

Adjacent sequences: A336920 A336921 A336922 * A336924 A336925 A336926

Keyword

nonn,mult

Author

Antti Karttunen, Aug 09 2020

Extensions

Keyword:mult added by Antti Karttunen, Jan 06 2023

Status

approved