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A304963 Expansion of 1/(1 - Sum_{i>=1, j>=1, k>=1} x^(i*j*k)). 2

%I

%S 1,1,4,10,31,82,241,664,1898,5316,15058,42374,119718,337432,952373,

%T 2685906,7578248,21376331,60306495,170120330,479922212,1353855927,

%U 3819280961,10774233218,30394408336,85743168417,241883489742,682358211402,1924947591447,5430317571250,15319043353639

%N Expansion of 1/(1 - Sum_{i>=1, j>=1, k>=1} x^(i*j*k)).

%C Invert transform of A007425.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%F G.f.: 1/(1 - Sum_{k>=1} A007425(k)*x^k).

%p A:= proc(n, k) option remember; `if`(k=1, 1,

%p add(A(d, k-1), d=numtheory[divisors](n)))

%p end:

%p a:= proc(n) option remember; `if`(n=0, 1,

%p add(A(j, 3)*a(n-j), j=1..n))

%p end:

%p seq(a(n), n=0..35); # _Alois P. Heinz_, May 22 2018

%t nmax = 30; CoefficientList[Series[1/(1 - Sum[x^(i j k), {i, 1, nmax}, {j, 1, nmax/i}, {k, 1, nmax/i/j}]), {x, 0, nmax}], x]

%t nmax = 30; CoefficientList[Series[1/(1 - Sum[Sum[DivisorSigma[0, d], {d, Divisors[k]}] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

%t a[0] = 1; a[n_] := a[n] = Sum[Sum[DivisorSigma[0, d], {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 30}]

%Y Cf. A000005, A007425, A011782, A129921, A174465, A280473, A304964.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, May 22 2018

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Last modified August 4 09:03 EDT 2020. Contains 336201 sequences. (Running on oeis4.)