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.

A340197 a(1) = 1; for n > 1, a(n) = Sum_{d|n, dA318833(n/d)-1) * A340197(d).

Original entry on oeis.org

1, 0, 0, 2, 0, 7, 0, 6, 6, 13, 0, 13, 0, 19, 22, 18, 0, 19, 0, 23, 32, 31, 0, 53, 20, 37, 24, 33, 0, 21, 0, 54, 52, 49, 58, 110, 0, 55, 62, 95, 0, 29, 0, 53, 52, 67, 0, 185, 42, 53, 82, 63, 0, 139, 94, 137, 92, 85, 0, 321, 0, 91, 74, 162, 112, 45, 0, 83, 112, 45, 0, 403, 0, 109, 82, 93, 136, 53, 0, 331, 114, 121
Offset: 1

Views

Author

Antti Karttunen, Jan 05 2021

Keywords

Comments

See comments and question in A340140.

Links

Crossrefs

Cf. A023900, A318833, A340140, A340367.

Programs

Formula

a(1) = 1; for n > 1, a(n) = Sum_{d|n, dA318833(n/d)-1) * A340197(d).

A340140 a(1) = -1, for n > 1, a(n) = Sum_{d|n, dA340197(n/d) * a(d).

Original entry on oeis.org

-1, 0, 0, -2, 0, -7, 0, -6, -6, -13, 0, -13, 0, -19, -22, -22, 0, -19, 0, -23, -32, -31, 0, -81, -20, -37, -24, -33, 0, -21, 0, -78, -52, -49, -58, -183, 0, -55, -62, -147, 0, -29, 0, -53, -52, -67, 0, -321, -42, -53, -82, -63, 0, -223, -94, -213, -92, -85, 0, -591, 0, -91, -74, -278, -112, -45, 0, -83, -112, -45, 0, -733
Offset: 1

Views

Author

Antti Karttunen, Jan 05 2021

Keywords

Comments

This seems to differ from 1-A318833(n) at the points given by A033987.

Links

Crossrefs

Cf. A023900, A033987, A318833, A340197, A340367.

Programs

Formula

a(1) = -1, for n > 1, a(n) = Sum_{d|n, dA340197(n/d) * a(d).

A340198 Dirichlet inverse of sequence f(n) = A319340(n)-1 = (A000010(n) + A023900(n) - 1), where A000010 is Euler Totient function phi, and A023900 is its Dirichlet inverse.

Original entry on oeis.org

1, 1, 1, 1, 1, -1, 1, -1, -2, -5, 1, -8, 1, -9, -13, -9, 1, -16, 1, -22, -21, -17, 1, -28, -14, -21, -20, -36, 1, -43, 1, -31, -37, -29, -45, -49, 1, -33, -45, -62, 1, -67, 1, -64, -64, -41, 1, -69, -34, -64, -61, -78, 1, -68, -77, -96, -69, -53, 1, -88, 1, -57, -96, -79, -93, -115, 1, -106, -85, -123, 1, -95, 1, -69
Offset: 1

Views

Author

Antti Karttunen, Jan 05 2021

Keywords

Comments

Conversely, the Dirichlet inverse of this sequence yields a sequence which is one less than A319340, i.e., pointwise sum s(n) = A109606(n) + A023900(n).
a(9796) = 0 is the only zero among the first 2^22 terms.

Links

Crossrefs

Cf. A000010, A023900, A109606, A319340, A340090, A340094, A340197, A340367.

Programs

  • PARI
    A023900(n) = factorback(apply(p -> 1-p, factor(n)[, 1]));
A319340(n) = (eulerphi(n)+A023900(n));
A340198(n) = if(1==n,1,-sumdiv(n,d,if(dA319340(n/d)-1)*A340198(d),0)));

Formula

a(1) = 1, for n > 1, a(n) = -Sum_{d|n, dA319340(n/d)-1) * a(d).
Showing 1-3 of 3 results.

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

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