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A336923
a(n) = 1 if sigma(2n) - sigma(n) is a power of 2, otherwise 0.
10
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.
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. also A336477 (analogous sequence for Fermat primes).
Sequence in context: A115954 A115526 A363343 * A239681 A054524 A110471
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Aug 09 2020
EXTENSIONS
Keyword:mult added by Antti Karttunen, Jan 06 2023
STATUS
approved