A372226 - OEIS

A372226

a(n) = Sum_{k=1..n} sigma_2( n/gcd(k,n) ).

1, 6, 21, 48, 105, 126, 301, 388, 567, 630, 1221, 1008, 2041, 1806, 2205, 3116, 4641, 3402, 6517, 5040, 6321, 7326, 11661, 8148, 13125, 12246, 15327, 14448, 23577, 13230, 28861, 24956, 25641, 27846, 31605, 27216, 49321, 39102, 42861, 40740, 67281, 37926

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OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Sum_{d|n} phi(d) * sigma_2(d).

From Amiram Eldar, May 20 2024: (Start)

Multiplicative with a(p^e) = (p^(3*e+5) - p^(3*e+4) - p^(e+3) + p^e + p^4 - p^2) / ((p^2 - 1) * (p^3 - 1)).

Sum_{k=1..n} a(k) ~ c * n^4 / 4, where c = zeta(3) * zeta(4) * Product_{p prime} (1 - 1/p^2 - 1/p^4 + 1/p^5) = 0.749582840863254826301... . (End)

MATHEMATICA

a[n_] := DivisorSum[n, EulerPhi[#] * DivisorSigma[2, #] &]; Array[a, 100] (* Amiram Eldar, May 20 2024 *)