A379485 a(n) = 1 if gcd(n,A003961(n))*gcd(sigma(n),A276086(n)) is equal to gcd(n,A276086(n))*gcd(sigma(n),A003961(n)), otherwise 0, where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.

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

Offset

1

Links

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

Index entries for characteristic functions.

Index entries for sequences related to prime indices in the factorization of n.

Index entries for sequences related to primorial base.

Index entries for sequences related to sigma(n).

Formula

a(n) = [gcd(n,A003961(n)) * gcd(sigma(n),A276086(n)) = gcd(n,A276086(n)) * gcd(sigma(n),A003961(n))], where [ ] is the Iverson bracket.

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A379485(n) = { my(s=sigma(n), x=A003961(n), y=A276086(n)); (gcd(n, x)*gcd(s, y))==(gcd(n, y)*gcd(s, x)); };

Crossrefs

Characteristic function of A379486.

Cf. A000203, A003961, A276086.

Sequence in context: A167501 A285533 A185175 * A322586 A147612 A323509

Adjacent sequences: A379482 A379483 A379484 * A379486 A379487 A379488

Keyword

nonn

Author

Antti Karttunen, Jan 01 2025

Status

approved