A379111 a(n) = 1 if bigomega(sigma(n)) is equal to omega(n), otherwise 0.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..102400

Index entries for characteristic functions.

Index entries for sequences related to sigma(n).

Formula

Multiplicative with a(p^e) = A010051(sigma(p^e)) = A010051((p^(1+e) - 1)/(p-1)).

a(n) = [A001222(A000203(n)) = A001221(n)], where [ ] is the Iverson bracket.

Mathematica

Table[If[PrimeOmega[DivisorSigma[1, n]]==PrimeNu[n], 1, 0], {n, 105}] (* James C. McMahon, Dec 17 2024 *)

Prog

(PARI) A379111(n) = (bigomega(sigma(n))==omega(n));
(PARI) A379111(n) = { my(f=factor(n)); prod(i=1, #f~, isprime(sigma(f[i, 1]^f[i, 2]))); };

Crossrefs

Characteristic function of A379112.

Cf. A000203, A001221, A001222, A010051, A023194.

Cf. also A324892.

Sequence in context: A355449 A058840 A266155 * A262683 A359816 A378729

Adjacent sequences: A379108 A379109 A379110 * A379112 A379113 A379114

Keyword

nonn,mult

Author

Antti Karttunen, Dec 17 2024

Status

approved