A334784 a(n) = Sum_{d|n} lcm(tau(d), sigma(d)).

1, 7, 5, 28, 7, 23, 9, 88, 44, 49, 13, 128, 15, 39, 35, 243, 19, 140, 21, 112, 45, 55, 25, 308, 100, 105, 84, 228, 31, 161, 33, 369, 65, 133, 63, 1064, 39, 87, 75, 532, 43, 183, 45, 160, 152, 103, 49, 1083, 66, 328, 95, 420, 55, 300, 91, 408, 105, 217, 61, 476

Offset

1,2

Links

Table of n, a(n) for n=1..60.

Formula

a(p) = p + 2 for p = odd primes (A065091).

Example

a(6) = lcm(tau(1), sigma(1)) + lcm(tau(2), sigma(2)) + lcm(tau(3), sigma(3)) + lcm(tau(6), sigma(6)) = lcm(1, 1) + lcm(2, 3) + lcm(2, 4) + lcm(4, 12) = 1 + 6 + 4 + 12 = 23.

Mathematica

a[n_] := DivisorSum[n, LCM[DivisorSigma[0, #], DivisorSigma[1, #]] &]; Array[a, 100] (* Amiram Eldar, May 10 2020 *)

Prog

(Magma) [&+[LCM(#Divisors(d), &+Divisors(d)): d in Divisors(n)]: n in [1..100]]
(PARI) a(n) = sumdiv(n, d, lcm(numdiv(d), sigma(d))); \\ Michel Marcus, May 10 2020

Crossrefs

Cf. A334579 (Sum_{d|n} gcd(tau(d), sigma(d))), A334783 (Sum_{d|n} lcm(d, sigma(d))).

Cf. A000005 (tau(n)), A000203 (sigma(n)), A009278 (lcm(tau(n), sigma(n))).

Sequence in context: A263825 A226661 A120404 * A146619 A059990 A213246

Adjacent sequences: A334781 A334782 A334783 * A334785 A334786 A334787

Keyword

nonn

Author

Jaroslav Krizek, May 10 2020

Status

approved