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

Author

Antti Karttunen, Apr 15 2021

Keywords

• nonn

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)

Crossrefs

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

Programs

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));

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