A364252 a(n) = 1 if n has no other prime factors than 2 and/or Mersenne primes, otherwise 0.

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

Offset

1

Links

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

Index entries for characteristic functions

Formula

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

a(n) = [A336467(n) == 1].

a(n) >= A336923(n) >= A364251(n).

Prog

(PARI)
A209229(n) = (n && !bitand(n, n-1));
A364252(n) = { my(f=factor(n)); prod(k=1, #f~, (2==f[k, 1] || A209229(f[k, 1]+1))); };

Crossrefs

Cf. A036987, A209229, A336467, A336923, A364251.

Characteristic function of A219174.

Sequence in context: A257196 A176137 A290808 * A385888 A190239 A120529

Adjacent sequences: A364249 A364250 A364251 * A364253 A364254 A364255

Keyword

nonn,mult

Author

Antti Karttunen, Jul 16 2023

Status

approved