A334782 a(n) = Sum_{d|n} lcm(d, tau(d)).

1, 3, 7, 15, 11, 21, 15, 23, 16, 33, 23, 45, 27, 45, 77, 103, 35, 48, 39, 105, 105, 69, 47, 77, 86, 81, 124, 141, 59, 231, 63, 199, 161, 105, 165, 108, 75, 117, 189, 153, 83, 315, 87, 213, 176, 141, 95, 397, 162, 258, 245, 249, 107, 372, 253, 205, 273, 177

Offset

1,2

Links

Table of n, a(n) for n=1..58.

Formula

a(p) = 2p + 1 for p = odd primes (A065091).

Example

a(6) = lcm(1, tau(1)) + lcm(2, tau(2)) + lcm(3, tau(3)) + lcm(6, tau(6)) = lcm(1, 1) + lcm(2, 2) + lcm(3, 2) + lcm(6, 4) = 1 + 2 + 6 + 12 = 21.

Mathematica

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

Prog

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

Crossrefs

Cf. A322979 (Sum_{d|n} gcd(d, tau(d))), A334783 (Sum_{d|n} lcm(d, sigma(d))).

Cf. A000005 (tau(n)), A000203 (sigma(n)), A009230 (lcm(n, tau(n))).

Sequence in context: A114396 A348483 A333556 * A102032 A086517 A346296

Adjacent sequences: A334779 A334780 A334781 * A334783 A334784 A334785

Keyword

nonn

Author

Jaroslav Krizek, May 10 2020

Status

approved