A343226 a(n) = gcd(sigma(n), n+A003415(n)), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.

1, 3, 4, 1, 6, 1, 8, 5, 1, 1, 12, 28, 14, 1, 1, 1, 18, 39, 20, 2, 1, 1, 24, 4, 1, 1, 2, 4, 30, 1, 32, 7, 1, 1, 1, 1, 38, 1, 1, 18, 42, 1, 44, 4, 6, 1, 48, 4, 3, 1, 1, 2, 54, 15, 1, 4, 1, 1, 60, 8, 62, 1, 2, 1, 1, 1, 68, 14, 1, 3, 72, 3, 74, 1, 2, 4, 1, 1, 80, 2, 1, 1, 84, 16, 1, 1, 1, 12, 90, 3, 1, 4, 1, 1, 1, 4

Offset

1,2

Comments

a(n) = n+1 iff n is prime (A000040). - Bernard Schott, Jun 01 2021

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n)

Formula

a(n) = gcd(A000203(n), A129283(n)) = gcd(A000203(n), A211991(n)).

a(n) = A000203(n) / A343227(n).

a(n) = 1 if n is squarefree semiprime (A006881). - Bernard Schott, Jun 02 2021

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A129283(n) = (n+A003415(n));
A343226(n) = gcd(sigma(n), A129283(n));

Crossrefs

Cf. A000203, A003415, A129283, A211991, A343227.

Sequence in context: A339964 A342915 A276433 * A030707 A349629 A254525

Adjacent sequences: A343223 A343224 A343225 * A343227 A343228 A343229

Keyword

nonn

Author

Antti Karttunen, Apr 15 2021

Status

approved