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.

A215195 Numbers n such that A143615(n) = sigma(n) where sigma(n) = A000203(n).

Original entry on oeis.org

1, 598, 1498, 54797260
Offset: 1

Views

Author

Naohiro Nomoto, Aug 05 2012

Keywords

Comments

a(5) (if it exists) > 10^8. - Hiroaki Yamanouchi, Sep 11 2014

Crossrefs

Cf. A000203, A143615.

Programs

  • PARI
    isok(n) = sum(m=1, n, if (gcd(n,m)==1, numdiv(m))) == sigma(n); \\ Michel Marcus, Nov 08 2014

Extensions

a(4) from Hiroaki Yamanouchi, Sep 11 2014

A215196 Numbers n such that A143615(n) = n.

Original entry on oeis.org

1, 3, 40, 576, 606, 8988, 10296
Offset: 1

Views

Author

Naohiro Nomoto, Aug 05 2012

Keywords

Comments

a(8) (if it exists) > 10^8. - Hiroaki Yamanouchi, Sep 11 2014

Extensions

a(6)-a(7) from Max Alekseyev, Aug 18 2013

A211932 a(n) = Sum_{ m=1..n and gcd(n,m)>1 } tau(m), where tau is the number of divisors function, A000005.

Original entry on oeis.org

0, 2, 2, 5, 2, 11, 2, 13, 9, 19, 2, 28, 2, 29, 25, 32, 2, 47, 2, 50, 35, 50, 2, 69, 19, 62, 41, 72, 2, 96, 2, 80, 59, 86, 47, 114, 2, 99, 72, 118, 2, 144, 2, 125, 107, 125, 2, 164, 31, 158, 100, 151, 2, 188, 71, 174, 112, 167, 2, 229, 2, 183, 151, 188, 87, 247, 2, 208, 142, 252, 2, 271, 2, 228, 203, 238, 85
Offset: 1

Views

Author

Naohiro Nomoto, Aug 05 2012

Keywords

Links

Crossrefs

Cf. A000005, A143615.

Programs

  • Maple
    A211932 := proc(n)
        local a,m;
        a := 0 ;
        for m from 1 to n do
                if gcd(m,n) > 1 then
                a := a+numtheory[tau](m) ;
                end if;
        end do:
        a ;
end proc: # R. J. Mathar, Aug 08 2012
  • PARI
    A211932(n) = sum(m=1,n,if(1==gcd(n,m),0,numdiv(m))); \\ Antti Karttunen, Jan 22 2025

Formula

a(n) = A006218(n) - A143615(n).

A143614 Triangle read by rows: A054521 * A051731 as infinite lower triangular matrices.

Original entry on oeis.org

1, 1, 0, 2, 1, 0, 2, 0, 1, 0, 4, 2, 1, 1, 0, 2, 0, 0, 0, 1, 0, 6, 3, 2, 1, 1, 1, 0, 4, 0, 1, 0, 1, 0, 1, 0, 6, 3, 0, 2, 1, 0, 1, 1, 0, 4, 0, 2, 0, 0, 0, 1, 0, 1, 0, 10, 5, 3, 2, 2, 1, 1, 1, 1, 1, 0, 4, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 12, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 0, 6, 0, 2, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0
Offset: 1

Views

Author

Gary W. Adamson, Aug 27 2008

Keywords

Comments

Left border = phi(n), A000010: (1, 1, 2, 2, 4, 2, 6,...).
Row sums = A143615: (1, 1, 3, 3, 8, 3, 14, 7,...).

Examples

			First few rows of the triangle =
1;
1, 0;
2, 1, 0;
2, 0, 1, 0;
4, 2, 1, 1, 0;
2, 0, 0, 0, 1, 0;
6, 3, 2, 1, 1, 1, 0;
4, 0, 1, 0, 1, 0, 1, 0;
6, 3, 0, 2, 1, 0, 1, 1, 0;
...

Crossrefs

Cf. A000010, A051731, A054521, A143615.

Formula

A054521 records the relative primes of n, indicated by a 1's in row n, 0 otherwise. A051731 = the inverse Moebius transform, in which 1's by rows indicate the divisors of n, 0 otherwise.

Extensions

a(96) and a(101) split by Georg Fischer, May 29 2023
Showing 1-4 of 4 results.

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

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