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 1-4 of 4 results.

A094100 Fit a polynomial of degree k-1 to column k of array in A048790, evaluate it at dimension n = -1.

Original entry on oeis.org

1, -2, 9, -64, 560, -5370, 53788, -555864, 5957685, -66459200, 763983132, -8919566196, 105678848821, -1286858544734
Offset: 1

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Comments

Might be thought of as number of rooted (-1)-dimensional "polycubes" with n cells, with no symmetries removed.

References

  • Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

Crossrefs

Extensions

a(9)-a(14) using Luther & Mertens's formulas added by Andrei Zabolotskii, Jun 27 2025

A094101 Number of rooted 8-dimensional "polycubes" with n cells, with no symmetries removed.

Original entry on oeis.org

1, 16, 360, 9104, 246020, 6940128, 201819688, 6003642144, 181770021702, 5581576203840, 173384554507648, 5438172832075920
Offset: 1

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Keywords

References

  • Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

Crossrefs

Formula

a(n) = n * A151834(n). - Andrew Howroyd, Dec 05 2018

Extensions

a(9)-a(12) from Andrew Howroyd, Dec 05 2018

A048980 Difference between number of nonprimes and primes in reduced residue system of primorial numbers.

Original entry on oeis.org

1, 1, 0, -6, -36, -196, -724, 7512, 366838, 11928316, 421130508, 14598816402, 584642184936, 25314953837836, 1128885572358548, 54492272309366314, 2950485568862138250, 213151926413154110951
Offset: 0

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Examples

			n=4, Q(4)=2*3*5*7=210, reduced residue system includes 48 terms:42 primes and 6 composites and 1: a(4)=6-42=-36.
		

Crossrefs

Programs

  • Mathematica
    Table[Function[P, EulerPhi@ P - 2 # &[PrimePi@ P - n]]@ Product[Prime@ i, {i, n}], {n, 0, 12}] (* Michael De Vlieger, May 08 2017 *)

Formula

a(n) = A048863(n) - A048862(n) = A048866(A002110(n)).
a(n) = A005867(n) - 2*A000849(n) + 2*n.

Extensions

Corrected and extended by Max Alekseyev, Feb 22 2016

A048982 Number of numbers which have a "prime-rich" reduced residue system (RRS) and binary order n.

Original entry on oeis.org

0, 0, 0, 1, 3, 8, 15, 22, 32, 50, 85, 80, 98, 84, 59, 37, 10, 2, 0, 0, 0
Offset: 0

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Comments

It is remarkable that in exponentially increasing ranges these occurrences increase to n=13 and thereafter decline to zero. So A048868 is believed to be finite.

Examples

			In binary order (A029837) zone of 7, i.e., in [65,128], 22 numbers belong to A048868: 66, 68, 70, 72, 74, 76, 78, 80, 84, 88, 90, 96, 98, 100, 102, 104, 108, 110, 112, 114, 120, and 126. The largest term is 90090. The largest 4 are divisible by 2310, the largest 28 by 210, and the largest 103 by 30.
		

Crossrefs

Showing 1-4 of 4 results.