A353945 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} tau(n)*x^n, where tau = A000005.

1, 1, 0, 0, -1, 1, -1, 0, 1, -2, 0, 1, -1, -2, 2, 1, -2, -2, 2, 0, -4, 0, 3, -3, 3, -3, -2, -1, 1, 8, -15, 0, 17, -14, -1, -3, 9, -5, -18, 23, -10, -18, 24, -17, -17, 18, 27, -48, -37, 72, 45, -119, -11, 148, -98, -28, 65, -57, 24, -95, 213, -363, -173, 704, -435

Offset

1,10

Links

Table of n, a(n) for n=1..65.

Formula

Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} x^n / (1 - x^n).

Mathematica

A[m_, n_] := A[m, n] = Which[m == 1, DivisorSigma[0, n], m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m - 1, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 65]

Crossrefs

Cf. A000005, A320779, A328775, A353923, A353947, A353948, A353949.

Sequence in context: A096568 A025862 A004540 * A379071 A089614 A064875

Adjacent sequences: A353942 A353943 A353944 * A353946 A353947 A353948

Keyword

sign

Author

Ilya Gutkovskiy, May 12 2022

Status

approved