A342671 a(n) = gcd(sigma(n), A003961(n)), where A003961 is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors of n.

1, 3, 1, 1, 1, 3, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 21, 1, 3, 1, 15, 1, 3, 5, 1, 1, 3, 1, 9, 1, 3, 1, 1, 1, 3, 1, 9, 1, 3, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 15, 1, 3, 5, 3, 1, 21, 1, 3, 1, 1, 7, 3, 1, 9, 1, 3, 1, 15, 1, 3, 1, 1, 1, 3, 1, 3, 1, 3, 1, 1, 1, 3, 5, 9, 1, 3, 1, 3, 1, 3, 1, 9, 1, 3, 13, 7, 1, 3, 1, 3, 1

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = gcd(A000203(n), A003961(n)).

a(n) = gcd(A000203(n), A286385(n)) = gcd(A003961(n), A286385(n)).

a(n) = A341529(n) / A342672(n).

From Antti Karttunen, Jul 21 2022: (Start)

a(n) = A003961(n) / A349161(n).

a(n) = A000203(n) / A349162(n).

a(n) = A161942(n) / A348992(n).

a(n) = A003961(A349163(n)) = A003961(n/A349164(n)).

(End)

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A342671(n) = gcd(sigma(n), A003961(n));

Crossrefs

Cf. A000203, A003961, A161942, A286385, A341529, A342672, A342673, A348992, A349161, A349162, A349163, A349164, A349165 (positions of 1's), A349166 (of terms > 1), A349167, A349756, A350071 [= a(n^2)], A355828 (Dirichlet inverse).

Cf. A349169, A349745, A355833, A355924 (applied onto prime shift array A246278).

Cf. also A336850, A354827/A354828, A355932.

Sequence in context: A086869 A348953 A095345 * A132468 A353235 A243915

Adjacent sequences: A342668 A342669 A342670 * A342672 A342673 A342674

Keyword

nonn

Author

Antti Karttunen, Mar 20 2021

Status

approved