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.

A348128 Product_{n>=1} (1 + a(n)*x^n) = 1 + Sum_{n>=1} x^prime(n).

Original entry on oeis.org

0, 1, 1, 0, 0, 0, 1, 0, -1, -1, 2, 1, 0, -2, 0, 1, 3, -2, -1, 0, 4, 0, -1, -4, 6, 2, 2, -10, 4, 4, 13, -15, -7, -2, 30, -7, -7, -33, 42, 8, 16, -70, 27, 22, 95, -116, -21, -39, 223, -61, -48, -261, 326, 51, 129, -581, 242, 109, 752, -932, -105, -330, 1806, -612, -240, -2140, 2750, 227, 1245, -4865
Offset: 1

Views

Author

Ilya Gutkovskiy, Oct 01 2021

Keywords

Links

Crossrefs

Cf. A000040, A002121, A010051, A030010, A147557, A305871, A305882, A308298, A328777, A348127.

A328777 Product_{n>=1} (1 + x^n)^a(n) = 1 + Sum_{n>=1} x^prime(n).

Original entry on oeis.org

0, 1, 1, 0, 0, 0, 1, 0, -1, -1, 2, 1, 0, -2, 0, 1, 3, -3, -1, -1, 4, -1, -1, -4, 6, 2, 2, -13, 4, 4, 13, -15, -5, -5, 30, -11, -7, -34, 42, 7, 16, -78, 27, 18, 95, -117, -21, -49, 223, -76, -40, -262, 326, 48, 135, -642, 242, 103, 752, -938, -105, -408, 1826, -732, -240
Offset: 1

Views

Author

Ilya Gutkovskiy, Oct 27 2019

Keywords

Comments

Inverse weigh transform of A010051.

Crossrefs

Cf. A000040, A000586, A010051, A305871, A308298.

Programs

  • Mathematica
    b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[a[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; a[n_] := a[n] = Boole[PrimeQ[n]] - b[n, n - 1]; Array[a, 65]

A348127 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} x^prime(n).

Original entry on oeis.org

0, 1, 1, -1, 0, -1, 1, -1, -1, -1, 2, 0, 0, -3, 0, 0, 3, -3, -1, -1, 4, -4, -1, -5, 6, 2, 2, -17, 4, 4, 13, -16, -7, -11, 30, -14, -7, -34, 42, 7, 16, -80, 27, 6, 95, -117, -21, -60, 223, -97, -48, -265, 326, 53, 129, -800, 242, 93, 752, -948, -105, -499, 1806, -853, -240, -2189, 2750, 124
Offset: 1

Views

Author

Ilya Gutkovskiy, Oct 01 2021

Keywords

Links

Crossrefs

Cf. A000040, A002121, A010051, A030010, A147557, A305871, A305882, A308298, A328777, A348128.

Programs

  • Maple
    N:= 20: # for a(1)..a(N)
P:= 1: a:= Vector(N):
for n from 1 to N do
  c:= coeff(P,x,n);
  if isprime(n) then a[n]:= 1-c  else a[n]:= -c fi;
  P:= series(P/(1-a[n]*x^n),x,N+1);
od:
convert(a,list); # Robert Israel, Mar 01 2022
Showing 1-3 of 3 results.

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

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