A329274 Expansion of 1 / (1 + Sum_{k>=1} phi(k) * log(1 - 2 * x^k) / k), where phi = A000010.

1, 2, 7, 24, 83, 286, 989, 3416, 11807, 40806, 141041, 487488, 1684971, 5823986, 20130299, 69579356, 240497727, 831269134, 2873243541, 9931234972, 34326861907, 118649239730, 410105717339, 1417511828340, 4899565424887, 16935125993974, 58535496103303, 202325291692972

Offset

0,2

Comments

Invert transform of A000031.

Links

Table of n, a(n) for n=0..27.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A000031(k) * a(n-k).

Mathematica

nmax = 27; CoefficientList[Series[1/(1 + Sum[EulerPhi[k] Log[1 - 2 x^k]/k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[(1/k) DivisorSum[k, EulerPhi[#] 2^(k/#) &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 27}]

Crossrefs

Cf. A000010, A000031, A070933.

Sequence in context: A021000 A003480 A020727 * A370477 A088854 A000777

Adjacent sequences: A329271 A329272 A329273 * A329275 A329276 A329277

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 11 2019

Status

approved