A334490 a(n) = Sum_{d|n} gcd(d, sigma(d)).

1, 2, 2, 3, 2, 9, 2, 4, 3, 5, 2, 14, 2, 5, 6, 5, 2, 13, 2, 8, 4, 5, 2, 27, 3, 5, 4, 34, 2, 21, 2, 6, 6, 5, 4, 19, 2, 5, 4, 19, 2, 19, 2, 10, 10, 5, 2, 32, 3, 7, 6, 8, 2, 20, 4, 43, 4, 5, 2, 40, 2, 5, 6, 7, 4, 21, 2, 8, 6, 11, 2, 35, 2, 5, 8, 10, 4, 19, 2, 22

Offset: 1

Author

Jaroslav Krizek, May 03 2020

Keywords

• nonn

Examples

			a(6) = gcd(1, sigma(1)) + gcd(2, sigma(2)) + gcd(3, sigma(3)) + gcd(6, sigma(6)) = gcd(1, 1) + gcd(2, 3) + gcd(3, 4) + gcd(6, 12) = 1 + 1 + 1 + 6 = 9.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A322979 (Sum_{d|n} gcd(d, tau(d))), A000203 (Sum_{d|n} gcd(d, pod(d)) = sigma(n)).

Cf. A000040, A007955 (pod(n)), A334491 (for product instead of sum).

Inverse Möbius transform of A009194.

Programs

Magma

[&+[GCD(d, &+Divisors(d)): d in Divisors(n)]: n in [1..100]]

Mathematica

a[n_] := DivisorSum[n, GCD[#, DivisorSigma[1, #]] &]; Array[a, 80] (* Amiram Eldar, May 03 2020 *)

PARI

a(n) = sumdiv(n, d, gcd(d, sigma(d))); \\ Michel Marcus, May 03 2020

Formula

a(p) = 2 for p = primes (A000040).

a(n) = Sum_{d|n} A009194(d). - Antti Karttunen, May 09 2020