A279888 a(n) = Sum_{k=1..n-1} sigma_3(k)*sigma_5(n-k).

0, 1, 42, 569, 4250, 22006, 88004, 293369, 845358, 2186376, 5145646, 11282966, 23143198, 45179324, 83905292, 150271993, 258816840, 433786483, 704268402, 1119633944, 1733618768, 2640037170, 3931060364, 5777392406, 8325691750, 11873200964, 16643954724, 23133008124

Offset: 1

Author

Seiichi Manyama, Dec 22 2016

Keywords

• nonn

References

• Jean-Pierre Serre, A Course in Arithmetic, Springer-Verlag, 1973, Chapter VII, Section 4.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001158, A001160, A013957, A279917.

Programs

Mathematica

Table[Sum[If[k == 0, 0, DivisorSigma[3, k]] DivisorSigma[5, n - k], {k, 0, n - 1}], {n, 28}] (* Michael De Vlieger, Dec 22 2016 *)
a[n_] := (11 * DivisorSigma[9, n] - 21 * DivisorSigma[5, n] + 10 * DivisorSigma[3, n]) / 5040; Array[a, 30] (* Amiram Eldar, Jan 07 2025 *)

PARI

a(n) = {my(f = factor(n)); (11 * sigma(f, 9) - 21 * sigma(f, 5) + 10 * sigma(f, 3)) / 5040;} \\ Amiram Eldar, Jan 07 2025

Formula

a(n) = (11*sigma_9(n)-21*sigma_5(n)+10*sigma_3(n))/5040.