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A334793 a(n) = Sum_{d|n} lcm(tau(d), pod(d)) where tau(k) is the number of divisors of k (A000005) and pod(k) is the product of divisors of k (A007955). 2

%I #10 Sep 08 2022 08:46:25

%S 1,3,7,27,11,45,15,91,34,113,23,1797,27,213,917,5211,35,5904,39,24137,

%T 1785,509,47,333637,386,705,2950,66093,59,811055,63,103515,4385,1193,

%U 4925,10085352,75,1485,6117,2584201,83,3113715,87,256085,183194,2165,95

%N a(n) = Sum_{d|n} lcm(tau(d), pod(d)) where tau(k) is the number of divisors of k (A000005) and pod(k) is the product of divisors of k (A007955).

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

%e a(6) = lcm(tau(1), pod(1)) + lcm(tau(2), pod(2)) + lcm(tau(3), pod(3)) + lcm(tau(6), pod(6)) = lcm(1, 1) + lcm(2, 2) + lcm(2, 3) + lcm(4, 36) = 1 + 2 + 6 + 36 = 45.

%t a[n_] := DivisorSum[n, LCM[(d = DivisorSigma[0, #]), #^(d/2)] &]; Array[a, 100] (* _Amiram Eldar_, May 12 2020 *)

%o (Magma) [&+[LCM(#Divisors(d), &*Divisors(d)): d in Divisors(n)]: n in [1..100]]

%o (PARI) a(n) = sumdiv(n, d, lcm(numdiv(d), vecprod(divisors(d)))); \\ _Michel Marcus_, May 12 2020

%Y Cf. A334662 (Sum_{d|n} gcd(tau(d), pod(d))), A334784 (Sum_{d|n} lcm(tau(d), sigma(d))).

%Y Cf. A000005 (tau(n)), A007955 (pod(n)), A324528 (lcm(tau(n), pod(n))).

%K nonn

%O 1,2

%A _Jaroslav Krizek_, May 12 2020

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)