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A087115 Convolution of sum of cubes of divisors with itself. 3
0, 1, 18, 137, 650, 2350, 6860, 17609, 39870, 83976, 162382, 301070, 522886, 885284, 1424468, 2254537, 3419448, 5143987, 7448874, 10750712, 15015872, 20948610, 28373444, 38539022, 50863150, 67454492, 87209316, 113326308, 143748766, 183759900, 229271536 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Ramanujan's Eisenstein series: P(q) (see A006352), Q(q) (A004009), R(q) (A013973).

REFERENCES

J.-P. Serre, A Course in Arithmetic, Springer-Verlag, 1973, Chap. VII, Section 4., p. 93.

LINKS

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

FORMULA

G.f.: (Sum_{k>0} k^3 * x^k / (1 - x^k))^2. a(n) = (sigma_7(n) - sigma_3(n)) / 120.

G.f.: ((Q(x) - 1) / 240)^2 where Q() is a Ramanujan Eisenstein series.

EXAMPLE

G.f. = x^2 + 18*x^3 + 137*x^4 + 650*x^5 + 2350*x^6 + 6860*x^7 + 17609*x^8 + ...

MAPLE

with(numtheory); f:=n->add( sigma[3](k)*sigma[3](n-k), k=1..n-1);

MATHEMATICA

a[ n_] := If[ n < 1, 0, (DivisorSigma[ 7, n] - DivisorSigma[ 3, n]) / 120]; (* Michael Somos, Oct 08 2017 *)

PROG

(PARI) {a(n) = if( n<1, 0, (sigma(n, 7) - sigma(n, 3)) / 120)};

(PARI) {a(n) = if( n<1, 0, sum(m=1, n-1, sigma(m, 3) * sigma(n-m, 3)))};

CROSSREFS

Cf. A004009, A001158, A013955.

Sequence in context: A056003 A239208 A114239 * A163707 A212154 A108680

Adjacent sequences:  A087112 A087113 A087114 * A087116 A087117 A087118

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 13 2003

STATUS

approved

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Last modified October 15 13:06 EDT 2019. Contains 328030 sequences. (Running on oeis4.)