cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, May 12 2022

Keywords

Crossrefs

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

Programs

  • 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]

Formula

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

A353948 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} phi(n)*x^n, where phi = A000010.

Original entry on oeis.org

1, 0, 1, 0, 2, -3, 4, -4, 4, -10, 14, -25, 30, -48, 48, -86, 128, -192, 286, -470, 578, -1000, 1386, -2423, 3172, -5198, 7102, -11994, 16414, -25820, 38056, -61444, 86658, -141564, 203396, -324640, 475536, -767110, 1100728, -1810752, 2601166, -4118166, 6114666
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2022

Keywords

Crossrefs

Cf. A000010, A320778, A328774, A353925, A353945, A353947, A353949.

Programs

  • Mathematica
    A[m_, n_] := A[m, n] = Which[m == 1, EulerPhi[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, 43]

A353949 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} mu(n)*x^n, where mu = A008683.

Original entry on oeis.org

1, -2, 0, -3, -1, 4, -4, -4, -7, 14, -10, -2, -5, 6, 19, -102, 70, -95, 138, -314, 174, 48, -70, -156, -797, 2028, -2048, 1989, -3479, 4277, -2080, -11462, 7923, -12448, 32218, -68038, 68683, -64844, 82847, -170573, -24942, 257846, -422887, 599115, -1225608, 2072993
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2022

Keywords

Crossrefs

Cf. A008683, A320781, A353926, A353927, A353945, A353947, A353948.

Programs

  • Mathematica
    A[m_, n_] := A[m, n] = Which[m == 1, MoebiusMu[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, 46]
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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