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A334783
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a(n) = Sum_{d|n} lcm(d, sigma(d)).
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4
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1, 7, 13, 35, 31, 31, 57, 155, 130, 127, 133, 143, 183, 231, 163, 651, 307, 382, 381, 575, 741, 535, 553, 383, 806, 735, 1210, 315, 871, 631, 993, 2667, 673, 1231, 1767, 3770, 1407, 1527, 2379, 1055, 1723, 1599, 1893, 1487, 1450, 2215, 2257, 2367, 2850, 5552
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OFFSET
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1,2
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LINKS
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FORMULA
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a(p) = p^2 + p + 1 for p = primes (A000040).
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EXAMPLE
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a(6) = lcm(1, sigma(1)) + lcm(2, sigma(2)) + lcm(3, sigma(3)) + lcm(6, sigma(6)) = lcm(1, 1) + lcm(2, 3) + lcm(3, 4) + lcm(6, 12) = 1 + 6 + 12 + 12 = 31.
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MAPLE
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N:= 100: # for a(1)..a(N)
V:= Vector(N):
for d from 1 to N do
t:= ilcm(d, numtheory:-sigma(d));
R:= [seq(i, i=d..N, d)];
V[R]:= V[R] +~ t;
od:
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MATHEMATICA
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a[n_] := DivisorSum[n, LCM[#, DivisorSigma[1, #]] &]; Array[a, 100] (* Amiram Eldar, May 10 2020 *)
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PROG
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(Magma) [&+[LCM(d, &+Divisors(d)): d in Divisors(n)]: n in [1..100]]
(PARI) a(n) = sumdiv(n, d, lcm(d, sigma(d))); \\ Michel Marcus, May 10 2020
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CROSSREFS
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Cf. A334490 (Sum_{d|n} gcd(d, sigma(d))), A334782 (Sum_{d|n} lcm(d, tau(d))).
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KEYWORD
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AUTHOR
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STATUS
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approved
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