A361466 a(n) = 1 if A017665(A003961(n)) is a power of 2, otherwise 0. Here A017665 is the numerator of the sum of the reciprocals of the divisors of n, and A003961 is fully multiplicative with a(p) = nextprime(p).

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

Offset

1

Links

Winston de Greef, Table of n, a(n) for n = 1..10000

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) = A209229(A341525(n)) = A361465(A003961(n)).

a(n) = [A348942(n) = 1], where [ ] is the Iverson bracket.

If a(x) = a(y) = gcd(x, y) = 1, then also a(x*y) = 1.

Prog

(PARI)
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A209229(n) = (n && !bitand(n, n-1));
A341525(n) = { my(u=A003961(n), s=sigma(u)); (s/gcd(u, s)); };
A361466(n) = A209229(A341525(n));

Crossrefs

Characteristic function of A355942.

Cf. A003961, A209229, A326042, A341525, A348942, A355943, A361465.

Cf. also A341605.

Sequence in context: A151666 A355681 A214284 * A191747 A330323 A280933

Adjacent sequences: A361463 A361464 A361465 * A361467 A361468 A361469

Keyword

nonn

Author

Antti Karttunen, Mar 20 2023

Status

approved