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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).
3
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
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)); };
CROSSREFS
Characteristic function of A355942.
Cf. also A341605.
Sequence in context: A151666 A355681 A214284 * A191747 A330323 A280933
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 20 2023
STATUS
approved